It's tough to plan a Traveller campaign concept ahead of time. Character creation isn't completely random, but it's close enough that any given idea might easily run aground on an ill-fate dice roll. Luckily, that same character creation will usually give you more than enough ideas to hang a campaign on. Mine's been largely shaped by the one player who stuck a 12 in Social Status and then went on to get three boosts to the attribute when he mustered out of Noble. My original ideas about them being an unruly crew of rogue's and scoundrels quickly moved over in favor of this Duke Marlow Burrin's political aspirations, and the campaign's been better for it.
That said, it does help to have some idea of the shape of the campaign, even if it's conceived at the table during character creation. (And with help from the players; incorporating their input can make them fiercely loyal to the game.) The Mongoose Traveller book has a few campaign ideas to start with, but here's a few more specific ideas to help get you going:
The Love Boat: The characters are of the mostly respectable sort, the players enjoy a little interpersonal intrigue, and the ship's outfitted for a pleasure cruise. Pick up passengers, take them interesting places, and inevitably get dragged into their weird personal problems. One week the crew gets hired to find evidence of adultery, the next, they're outrunning bounty hunters and learning too-late about a passenger's criminal past.
The Voyager Knock-Off: Mis-jumps are a hazard in any game, and if you want a short-ish campaign with a set end point, a really bad mis-jump makes a good option. Stranded in an unknown part of space, all the characters want to do is get home, but they're broke. Adventure (and hilarity) ensues. You might work with each player to come up with a specific reason why everyone wants to get home now (Mary Jane will marry another man! The family farm will be repossessed!) or you can leave open the idea that they'll decide this part of space isn't so bad, and settle down into a comfortable existence as traders or freelancers. (And, simultaneously, a more long-term campaign.) The best part of a game like this is it gives you an excuse to throw in a lot of really strange stuff, to keep up the idea that the gang is far from home.
Space Ship Rockstar: This works just as well in space as it does with vampires. The crew is a band (famous or not) "on tour," hopping from planet to planet and holding concerts as they go. There's a couple of different approaches that would make this adventure-worthy. The band could be the Scooby Doo type, always getting involved in trouble on the way to, from, and at the venue. Or the game could focus on the trouble they go through to get paid: all those backwoods planets always have something that's got to get fixed before they'll have the promised cash on hand. Perhaps the most promising option is that the band is cover for another activity, whether it's bounty hunting, trouble-shooting, or smuggling.
Home, Sweet Home: There's no reason your players have to be the itinerant wanderers with a spaceship. Instead, they could be in charge of a space station themselves. Every week, they deal with a different batch of weirdos coming through, causing problems for quiet folks. This also gives them the opportunity to get a lot more involved with whatever the local problems are. Other variations on this option include all the usual possibilities of an urban campaign, (detectives, local politicians, or plain old adventuresome trouble-starters) set in a city that's a major hub of space-trade to allow for lots of Traveller goodness, or even a wilderness exploration game, where the players have been tasked with mapping and taming a wild planet.
The Lost Civilization: Whether it's alien or ancient human, exploring the ruins of another time spread across a sector or subsector makes for a good unifying hook for an exploration and study-based game. They might have been tasked with it by a higher authority, or simply gotten curious; either way, an interlocking series of ruins, with plenty of mysteries to uncover and solve, can be very engaging to a certain type of player. This one plays pretty well with a lot of other more general concepts, too; just drop in a ruin every so often, in between their other adventures.
Big Game Hunter: Travel to distant planets, track down the most exciting local wildlife, and kill it. (Or escort some rich nobles with plans for the same.) Another one that could fit inside a regular campaign without much difficulty, this one could work as a campaign on its own if the players like the idea of developing reputations as some of the best and most dangerous hunters in the galaxy. Beyond just coming up with new and more interesting critters, there's a number of variations that would make this kind of mission interesting: perhaps the creatures are protected by the Imperium for some reason, worshipped by the locals, or more valuable alive than dead. The crew might be tasked with recording the creature's rarely heard cry before they bag it, or have to discover the fates of the last group of fools to go after it. This would also be fun to reverse: perhaps the characters are a far-future version of Greenpeace, out to stop hunters (and other sorts of interplanetary despoilers) by any means necessary.