• 
  Trade: as much as can automate trivial tasks, if you want to be sure that your goods are delivered and paid in proper order and for the right price, it is better if you, merchant, travel with the goods. Along the trip you can also catch information which can help your business or that can be sold for a good price later on.


• 
  Diplomacy: Waiting years just for having an answer to an "Hello Dimitri" is not the most effective way to settle a quarrel which can escalate, better spend few years once and talk face to face. Also, this would prevent hackers to spoil the communication.


• 
  Exploration/tourism: The UV shining beaches on Sgombugulus IV are the non plus ultra for rich wannabes who want to boost their social media accounts at the cost of few thousand credits. And don't forget the Methane falls on Niagara VI!


• 
  Espionage: It might be about knowing accurate information on the industrial strategy of one of your competitor, or about uncovering the secret recipe of that soda drink or even knowing what are the rumors about the foreign politics of Madonius, having a pair of eyes and hears in the right place allows you having information not readily available via official media.

It Won't

I believe that Post-Colonial Interstellar Travel will be relatively uncommon event for a number of reasons...

• A great advantage of colonizing worlds is that it finally defeats one of our species' oldest threats: the pandemic-capable fatal infection. Finally, the human race is not facing extinction at the hands of a single organism. Unless that organism joins us on our journey to the stars. If interstellar travel is uncommon, then every colonized planet becomes a quarantined safe zone from the biological treats of the rest of the universe.



• 
  

  Secondly, it is possible that the time-dilation issues which complicate fractional light speed travel will continue (or even intensify) in FTL. Anyone choosing to travel between stars will lose their home world to the past. The people and culture which they leave behind will be history should they ever return. All interstellar journeys are likely to remain one-way tickets.

  
  
  

  Additionally, time dilation makes travel between stars dangerous on a political level. At the time of your departure, you may have reasonable proof that the government of your target planet will be amenable to your arrival, but a lot can change during a journey, which from the point of view of your destination may take hundreds of years. To put this in perspective, if an FTL ship arrived today with a subjective time dilation of only 300 years, the world they would be expecting to find would be preindustrial. If their travel visas had gotten lost during the last 30 decades, they might find themselves welcomed by the business end of our Star Wars defense satellite lasers.

  
  


• 
  

  Finally and perhaps most importantly, post-colonial interstellar travel is unnecessary. Throughout our history, we have repeatedly built thriving societies which met all of our species needs, using only the resources of a single planet. In the near future, we will start mining our solar system for its riches and there we will likely find that everything our species will ever NEED, is already here in orbit of our single star.

  
  
  

  Every profession which has ever existed is the product of a single planetary society. Every great artwork, great writing or great invention is the product of human minds which never left our planet's orbit. Whatever happiness and fulfillment which humanity has found has all been found right here. And the same will be true of all the other planets we will someday own.

  
  

Humans are home(world) bodies. They tend to stay where you plant them.

The general answer is going to be some form of gig job. These are short, temporary jobs that require the person (or team) to be on site.

Note: "temporary" could still be measured in earth years

These jobs are not permanent positions. However, the job requires a specialized skill that requires the person to be on site and the job can't come to them.

A few examples

• Auditors
  
  
  • government auditors
  
  
  • "new boss" checking out the factory
  
  


• Negotiators ( L.Dutch )
  
  
  • Diplomats
  
  
  • traders
  
  


• Diagnostic Engineers
  
  
  • the specialist team sent to fix a slight misalignment of your Death Star cannon
  
  
  • the team sent to investigate a spaceship crash
  
  
  • doctors that specialize in outbreaks of space plague.
  
  


• Entertainers
  
  
  • Ringling Brothers and Barnum and Bailey would have all sorts of animals to show off.
  
  
  • The curator for the traveling exhibit of "The Mummies of Zuban 5"
  
  
  • Galactic Cup contenders (sports)
  
  


• Vacationers ( L.Dutch )


• Explorers ( L.Dutch )
  
  
  • xeno-biologists
  
  


• Those that take advantage of poor enforcement of interstellar warrants
  
  
  • space pirates ( my first answer )
  
  
  • drug lords
  
  


• Those that enforce interstellar warrants
  
  
  • Detective Billy Mack from the star system Texas
  
  


• Humanitarian
  
  
  • red-cross/red crescent
  
  
  • U.N. peace keepers
  
  


• not-so-humanitarian
  
  
  • Blackwater Security Consulting
  
  
  • really big game hunters (eg T-Rex hunters/Meg fishers)
  
  


• lifestyle choice (edit - added this one)
  
  
  • nomads
  
  
  • gypsies
  
  

Almost no one under these conditions will travel

(average speed is 4 times the speed of light)

That means a year of travel from here to Earth's nearest not-the-sun star. Calculating time ship-board is meaningless, as once you've got FTL travel time dilation calculations don't work. Usually in these situations Ship-Time and Universe-Time flow 1:1 (because fiction!), which would mean a year on board for those people making the trip. Not exactly...thrilling stuff. Just keeping the crew fed is going to require a significant amount of cargo space.

At such distances and time scales, the only communication (e.g. letters) are going to be of sporadic personal or scientific in nature ("colony's going well, how have you been?"), albeit expensive (most letters will likely travel as negligible bulk on a cargo ship carrying a few million tons of something else). You won't have an effective "galactic" government that can control and enforce laws: remember the turnaround time on stuff like "help we're being invaded by aliens" is 2 years (even if the crew experiences no time!) and things like "You aren't following our laws, prepare to be invaded" are virtually meaningless. What's central authority going to do, show up in 4 years to put down a rebellion that's been over for three?

You could have trade, but it'd be for either resources you literally can't get (but if a delivery goes missing you'll survive: next one's not coming for a year). Even at 4:1 time dilation it would still be 3 months ship-board journey for every 4 light years traveled, which is almost comparable to current ocean shipping (where are small, often can't even communicate in a single language, and live in comparative squalor; its been compared to living in prison).

but have only densely colonised the star systems with 15-20 lightyears of Sol.

I...hate to tell you this, but that's like 4 potentially habitable star systems in that range. There's about 150 stars within that distance from Earth but most are red or brown dwarfs:

Nearby Celestial Objects by Type, Number, and Mass

Spectral or Number Sum of min
Luminosity Type within 20ly solar masses

O - Blue Stars 0 0.00
B - Blue White Stars 0 0.00
A - Bluish White Stars 2 3.84
F - Yellowish White Stars 1 1.50
G - Yellow-Orange Stars 7 6.76
K - Orange-Red Stars 15 11.84
M - Red Stars 88-90 21.32
M,L,T, Y - Brown Dwarfs 15-30 <1.20
D - White Dwarfs 7 4.30
Total Objects > 150 > 51.46

The 8 yellow stars are pretty much your only targets. Using Wikipedia's list of exoplanets we find 5 "potentially habitable" ones within 15 light years and 2 more out to 20 and another 3 ranging out to 30ly. That's pretty sparse with grueling ~8-12 year travel times (one side of inhabited space to the other); even between nearest-neighbors it might be as much as 4 years.

The only fiction I can think of that featured space travel on these kinds of time scales is The Deepness in the Sky where the Qeng Ho (humans of primarily Chinese decent) slow-boat it from system to system, trading where they can, helping inhabited planets rebuild after the collapse of civilization where they can't (because in a few hundred years they will be worth trading with again). And they primarily trade in technology. Not gadgets, but blueprints. Knowledge. They'll buy and transport things too, but those are purchased by the Qeng Ho for use by the Qeng Ho.

They do it as a safety net against humanity nuking itself into oblivion and going extinct, not because its profitable. As a result, they have a massive knowledgebase capable of kick-starting any planet to reasonable levels of technological comfort in decades (instead of millennia). Doesn't matter what you have access to, the Qeng Ho can work out an action plan, give you the right tech, and come back in a hundred years to see what Neat Stuff you invented while they were gone.

Because people want to

It has always been a little curious to me why people, whenever this question comes up, assume that since there are few rational reasons to travel between the stars (other than the mentioned one-way colony transports) people won't do it.

I know it's anecdotal, but of all the people I know (including myself) that have traveled recently, not a single person had a rational reason to do so. They traveled for leisure, they traveled to explore, they traveled hoping to find (even if temporary) a better place, they traveled hoping to escape (even if temporary) their current situation. Not one of them had a reason to travel that @HenryTaylor wouldn't be able to argue is unnecessary.

If you have ever met a backpacker you should know that travel is far more than a means to an end. Why would someone leave their family and all the comforts of home for over year, to basically live like a homeless person amidst strangers in a foreign land? Why did the mars one scam get 2700 applicants? Because people don't care about rational arguments, they care about the prospect of adventure and the possibility of simply being in another place. Even if odds are that place is worse than the place they departed from.

Travel is not mandated by circumstances, it is sought after by humans in the same way love is sought after by humans. Not because we need it to survive, but because we need it to feel alive.

Getting Rid of People You Don't Like

Lets say you run a planet whose main industry specializes in ultra-high end technological goods. Fully immersive VR sets, star-ship nav-computers, automated toaster dog walker combos etc etc. Business is good, trade is strong, and your people are happy. Well... most of them. A Luddite cult of anti-tech extremists keep insisting that you revert the planet back to it's natural state and rebuild a new naturalistic society based on smoking space weed and writing stream of consciousness novels. Now, these people haven't started anything violent or anything overtly disruptive yet but you can see it from here. Stock prices are already dropping a few points in anticipation of the violent riots and images on the news of your police force hosing down hippies with space pepper-spray. So, why not find them a new planet, we'll name it neo-nirvana, and we'll even bankroll a ship and colonization effort to get them off our planet and out of our hair. (Or maybe just have the secret police round them up and send them against their will if you wanna go the dystopian route.)

This method is how a significant portion of the planet was colonized by the European powers. Criminals along with political, religious, and racial minorities who were causing problems by existing and not agreeing with whatever the leadership wanted were usually quietly shipped off to new continents. Its a highly effective way to colonize new places and get rid of the people you don't like at the same time.

getting on or off a planet/habitat/station that has warrants out for
your arrest is tricky but otherwise travel is normally easy,
interstellar warrants are exceedingly rare; they're too awkward to
enforce

This screams:

Space Pirates

Your base of operations is in one star system; you raid other star systems as you desire.

You could raid the star system that hosts your base of operation. But, they'll have a warrant out for your arrest ASAP. This conundrum forces you to travel to other star systems to do you job.

Since you don't have a warrant at your base star system, you can come and go as you please. Since warrants are too awkward to enforce, you don't have to worry (too much) about getting one from a different star system. And if your base star system does receive one, bribery works wonders. If that doesn't work, you can easily move your base of operation to a different star system.

Travel Agent

A friend of mine professionally is required to visit and write about places for her job.

She travels all the time.

A few months at a time of travelling wouldn't be unreasonable when you need to explore and write about entire planets at each destination, you wouldn't return home though, you'd write the articles and send them on with the next ship headed to your employer. I'd imagine you'd travel with at least a couple other people though, cover more ground, look out for one another in strange cultures and frontier worlds.

On that note:

Writer

You don't really need to travel to be a writer, but it's not uncommon to use Travel as a way to get away from distractions.

Amtrak have actually provided a special Writer's Residency Program for exactly this purpose.
Hypothetically spending a few months aboard a ship would be a great way to complete mid/long term projects without distraction.

Courier

Some items simply cannot be trusted to unknown hands. A Parcel going via a starship might pass through the uncaring hands of dozens of deck-hands and dock-workers, postal workers and minions before finally getting to its destination.

Some things are worth paying extra for, and having someone babysit your critically important documentation or prototype technology all the way to its intended recipient might cost a fortune, but for an interstellar corporation paying through the nose for a trusted courier may well be worth it.

Journeyman

In some parts of europe there is an old tradition of travelling and apprenticing to a Master Craftsman. This is typically a single static role, but there's also a travelling variant where the journeyman migrates from town to town to learn many skills from multiple craftsmen.

Borrowed from Wikipedia:

In parts of Europe, as in Late Medieval Germany, spending time as a wandering journeyman (Wandergeselle), moving from one town to another to gain experience of different workshops, was an important part of the training of an aspirant master. Carpenters and other artisans in German speaking countries have retained the tradition of traveling journeymen even today, but only a few still practice it. In France, wandering journeymen were known as compagnons.

The future equivalent might be someone travelling from world to world, experiencing different cultures and learning unique trades of those worlds in order to gain life-experience before settling down to a particular trade and lifestyle.

If there are any interstellar governments they are likely to have space navies and also armies and marines.

Naturally an interstellar government would require that that anyone who is drafted into or voluntarily joins the military and naval forces be shipped to another system to garrison that system. Nobody would be permitted to be part of the garrison of their own system. Thus if their own system starts to revolt they won't be tempted to join the rebellion or be forced to crush the rebellion.

Malthus.

Now, it might not be starvation, but to a certain extent there will be better opportunities in some eras of a solar system colonization than there are elsewhere.

With a 40 light year diameter, it is 10 years to go to any other system. It turns out that system X has a great demand for asteroid base construction crews, and 10 years there will earn you a fortune back here.

So you pick up your family (or yourself if single), blink there, work for 10 years in the crappy conditions for great pay, then blink back. You now have a serious nest egg.

It is possible some systems have serious overpopulation issues and others are underpopulated; moving to become a colonist then becomes attractive. Move to planet X and get your own 100 km^2 ranch!

Generally, there are serious population flows for economic reasons on Earth when the income on one side reaches 2x the income on the other. With the time gap you may require a bit higher income multiplier, but it probably still exists.

A second possibility is that people can use this to exploit the most powerful force in the universe using the time-skip.

You may have projects that take decades to complete; building asteroid habitats, domes, terraforming bodies, disassembling comets, etc. If they can be done via automation or by low paid workers, the wealthy might want to start those projects off then skip forward in time. Have projects in two solar systems 5 years apart. Spend 6 months in one, jump to the other, spend 6 months, jump back.

After 4 years subjective you'll have 40 years of progress on both projects, done by a mixture of the fast-time underclass and robotics.

Drop it to 1 month each stop and you are living at a 60:1 time ratio. Over 20 years you get to experience 1200 years of profit from your endevours.

Compound interest of investments and projects can turn you into a hegemon. With a thermodynamic distribution of wealth and no practical limit to their lifespan, these temporal kings and queens will rule over the economies of the settled system from their jump-ship thrones.

Their children, raised by entire cities dedicated to the line, will compete and work towards the success of each petty ruler's economic empire. Those that succeed will in turn be lifted up to the near immortality of jump-time.

Of course, this will take a long time to pull off. Early in the human empire's history there will be a few people starting on it. And many will fail, as economic and political tides shift under their feet while they jump cross the universe.

Short of revolution, eventually capital itself becomes a monopoly of the temporal kings. They can afford a ROI that is tiny compared to anyone else as they accellerate their forward time travel, and they stitch up all of the capital and squeeze out everyone else.

You could imagine something akin to share cropping, but with all money. Like a feudal system where all the land is owned by the nobles and you cannot produce food or survive without their consent, shortly (in terms of the kings) all capital (money) could be owned by the temporal kings.

The temporal kings are unable to actively manage "all money" effectively, much like nobles are unable to farm their own land, so they'd permit share croppers to use their money in exchange for giving (say) 90% of the profits back to the real owners.

The leasure-based world would choke, as more and more resources get claimed for absentee landlords. Those who don't engage in generational savings end up crowded out of the resource marketplace. The temporal kings don't consume anything, so their amassed fortunes just keep on growing. Excess resources pile up, but the kings are willing to wait a few centuries for them to be used.

People who aren't useful to the temporal kings stop being allocated resources. When they want to buy something, like an asteroid or a robot farmer, they find that the temporal kings offer better terms for it. Individual kings start long-term plans to near monopolize commodities, like food/security/oxygen, with a high marginal incentive to purchase. Ogopolies form, and the kings have more in common with each other than they do with the mayflies.

In the end, economic production nearly shuts down. The kings continue to live in relavistic time. Servants come along with them. The mayflies are long gone, their buzzing faded into history. Long term projects, like terraforming mars into a garden, are within the grasp of individual kings. At 1 hour every 40 years, over a year the king can see 1/3 of a million years pass.

Huge automated infrastructures grind away at shooting comets at Mars, warming it with massive solar mirrors, and seeding it with life. When bugs happen, a prince goes into 1 day:40 year time, and his servants go into 1 month:40 year time, and their servants go into 2 year:40 years, all the way down to mayflies created and supervised to fix the problem.

There are reasons to travel that aren't specifically economic in nature. Other answers point out that artists may choose to travel to share their work. Others include hands-on type of training such as surgical techniques, new forms of meditation or religion.

Many difficult journeys throughout human history have been made to fulfill religious purposes. Pilgrimages, missionaries visiting remote tribes to evangelize, religious conclaves and such.

With all the new societies created, new branches of knowledge, philosophies, organizational approaches will be developed. Some of them will prove to be far more successful than what exist on other worlds. Things that take decades to learn in-person will not translate well to light-speed communication between star systems light-years apart.

People who want to travel to the future

If the cost of a round trip ticket that takes days of ship time but gets you back home decades later is less than your living expenses for those decades, you could sell everything, invest it all (apart from what you spend on the ticket), and come home rich. Also, you'll be in the future.

When Humans are More Useful than Letters

High Courts

If your hypothetical civilization has courts that have jurisdiction over multiple solar systems or indeed the entire civilization, then it would be necessary (due to a lack of real-time FTL communication) to transport individuals important to the trial to the location of the court - or to move the court to them! Either way, motion is necessary.

Absolute secrecy

Imagine that you are an incredibly wealthy trade mogul. Your starships move between systems carrying countless materials, and it is rare that anyone from your company other than crews do so. However, you have extremely important information that requires the utmost secrecy. You don't trust the interstellar mail service, digital files carried by them, or rank and file crew members to carry it. So you or someone very close to you must cross the vast expanse due to this extenuating circumstance.

Interstellar organizations

If your hypothetical civilization has a central government, or really any interstellar organizations, then it may send individuals to investigate questionable practices happening within their organization on a certain planet, or to send human resources to a faltering branch that needs help and management.

Unique Experts

Suppose that on planet X, they mine a particular gas that isn't available anywhere else. Or it wasn't possible. Things have changed; pioneers have discovered planet Y, which has the exact same gas! The problem is that they have no idea how to mine it or how to coordinate their mining or what the best economic policy about it would be. So they might want to ship over an expert from planet Y.

Education

No experts from planet X are willing to come and help out planet Y? No problem! Just send your smartest person to get educated over on planet X and bring their knowledge back.

Diplomacy

It is very hard to negotiate treaties and trade deals via letter.

Etc.

Personal Reasons

Travel to the Future!

Someone would want to. We're curious creatures.

A more compelling reason to do this is for severe medical conditions with no modern cure; you might as well skip ahead and enjoy the presumably more advanced medical science of the farther future.

Some rich person would definitely do this in search of an eventual cure for mortality.

Another reason to travel to the future would be to wait for a more friendly political climate. Cyborg rights may not be quite up to scratch on planet X, so a bunch of sufficiently wealthy cyborgs may arrange to travel back and forth until their home world is more friendly to them.

A criminal may also wait for a more friendly climate for entirely more illicit reasons.

There may also be economic reasons; waiting until an investment or bank account grows very large by artificially traveling to the future. (though some nations may outlaw this for its potentially destabilizing effects.)

Tourism

There are certain features of Earth so epic and so fascinating that even an interstellar citizen may want to see them, especially since interstellar travel is cheap. Things like the Grand Canyon. It's not unreasonable to assume that we may find similarly amazing natural features on other planets which would draw visitors.

Another reason to engage in tourism is for the sake of history. Some people may wish to go to particular historic sites on other planets, Earth especially.

Religious Pilgrimage

Much as Muslims today embark on the Hajj to Mecca, Muslims of the future may do the same. Yet other religions may have similar convictions about particular places. Followers would be very motivated to engage in interstellar travel.

Refugees

Individuals ruled over by an unfriendly government will obviously want to leave. Interstellar travel is one way of doing that. Still, they may initially move to another country on the same planet, but the government of the country will not necessarily want to take them in. The easy, relatively humane solution for the government receiving them? Ship the refugees to another planet!

And suppose that a horrific disaster occurs on planet A, and their ecology all but collapses, and almost everyone dies. There's nothing left to support the survivors, but there are a few ships still docked. I can't imagine most of the remaining survivors would wish to stay.

Fugitives

Unsafe on your current planet, for any reason? Leaving it entirely makes it much, much harder for anyone to pursue or even find you.

Ideology

People who wish to live in a place that matches their ideology may move to a planet where their ideas are well-received.

Economic Opportunity

Planet X has run out of gas! Oh no! Well, good thing the industry is going strong on planet Y. Might as well move there.

Curiosity

Why not?

Etc.

Permanent Relocation

Travel is quite "cheap" since even though it takes a long time from an outside perspective but takes zero time from the point of view of the traveler.

The time cost must be counted in "lost years." There will be very few travelers who have wage type jobs. Also, don't expect that job to still be around in X years.

So, vacations are only for those who don't have to work for their money. Even then there is a significant risk for the wealthy. What if conditions change and they are not around to react to the changes? Imagine coming back after the real estate crash. So only those with the most stable foundations will likely risk a vacation of that sort.

Most travel will likely be permanent or semi-permanent relocation. If you aren't expecting to come back (or expect to restart from scratch upon return), the time cost is minimal.

Another issue is the risk of innovation. When you get back, everything you know may be outdated.

Look at the filk song "Pushin the Speed of Light" (youtube) for an example of the time cost.

Escaping Exploitation

There are always those who scramble in search of a better life, away from the yoke of exploitation, unfair treatment or at least the perception of such. The earliest European settlers to what we now call America come to mind here. Such grievances can based in religion, politics or economics depending on what your story needs.

Planting Flags

Armed conflict on a large scale might be unheard of, but presumably there is still non-violent competition between political blocs. The advent of safe FTL travel would trigger a gold rush of sorts(at least initially) as all the powers seek to claim as much territory as possible, if only because they're afraid of losing out. With a galaxy for the taking, status and prestige can easily become tied to how many planets/systems you've occupied.

WAR

Let's just be honest, someone's going to want to try it.

Mining

As dumb as unobtain was in Avatar, it's actually grounded in engineering principles. If for some reason a rare material that solves a lot of problems in terms of engineering is discovered in some galaxy that takes 50 years to get to, some one is goin to want to travel 50 years to go get it. Keep in mind that these materials could make some very stupid things possible, and that with the human population likely ballooning after being able to fill multiple solar systems - not just planets - statistically speaking, there's probably going to be one rich person dumb enough to try getting it.

Just think about what a large asteroid's worth of anti-matter could do. There might not really be a reason to go get it, but given a large enough population someone's probably going to take the money hole "bait".

Professions which can't possibly be practiced in a single solar system

That would be any job that studies a facet of the cosmos, with exo in front of it. E.g., exobiologist, exochemist, exogeologist... etc. If they want to be on the cutting edge, leaving the solar system is literally one of their job requirements.