My groups loved to do things like:
Go to the planet, rob the bank, leave evidence making it look like the local druglord did it, then leave.
Run guns to the rebels fighting the large interstellar [pick one].
Misjump, crew injured, drives damaged, where the heck are we / repair, survive, get out.
Go to the distant world where the old wise man who wrote the holy scrolls acts like a drunken zen master, spilling the secrets of one possible universe, which they find out is wrong, which they find out is really right, which they find out both and neither are true.
Crash / blow up / sabotage the ship, wrecking the port, and escaping...sometimes.
Rip off / get ripped off by the megacorp's goons, and the resulting multi subsector chase / capture.
Best adventure, hands down: Across the Bright Face, with lots of combat, and air leaking, food, water and energy running out. Choose lots to see who gets offed because you ran out of one of the former, and can't make it back to the port otherwise. I always thought if Traveller was going to be a movie, that'd be a great start as a script.
Go to strange alien world, deal with the cargo, get liberty ashore, get caught up in some scam / plot / scheme, usually supplied by the "Hot Chick from the Bar" (tm).
Firefight, and mayhem aboard a huge passenger liner, "Titanic / Poseidon Adventure" in space."
Search for Anagathics / Psionics / Artifacts...
Really too many ideas to list.