Since you did not mention anything about your tastes, I'll just list every Vita game I liked (PSP and PSOne games excluded):
- Persona 4 Golden. A MUST BUY. This is the game I bought Vita for. Even if you did play the PS2 original I'd urge you to buy it. If you don't know what's it about, here is a quick summary: It is a turn based JRPG with dating sim elements about a high-school student who moved to another city and at the same time in this city a serial killer appeared. Soon, you discover that things are a tad bit more complicated than that. Now you have to travel to "TV universe", but also manage your ordinary life (which is interesting thanks to social link system).
It deals with rather complicated things such as not being accepted, being alone in this world, homosexuality and so on and on. A masterpiece of a JRPG. Playing previous games is in no way required to enjoy and understand this one.
- Zero Escape: Virtue's Last Reward. a Visual Novel/ Puzzle room game about 9 people kidnapped and frced to play a game. Can't say more because of spoilers. If you like interesting stories about science, time travel, scientific paradoxes and just complicated ones AND complicated but not ridiculous puzzles, then dive in. Also it is worth mentioning that it is a sequel to a game called 999, which was released on 3DS and while (just like with P4G) playing previous game is not required, but is recommended (at the very least in form of watching a LP). Also, sequel is to be released soon.
- Danganronpa 1 and 2. Well, since you are interested in UDG, playing those 2 is only logical. The basic gist of both games is that a group of students are locked into a place and soon they have to investigate murders. You liking characters depends on how well you can stomach japanese tropes (gothic lolita, sexy sportsy dumb bimbo, protag that always speaks of hope and friendship, etc.). The overall story is pretty meh, bad the cases themselves are really interesting.
- Gucamelee!. Basically, a really fun metroidvania where you play a mystical Luchador. Great gameplay, great art, great music, challenging and oh so nice to actually play.
- Soul Sacrifice, Toukiden and Freedom Wars. Those three are Monster Hunter analogues. The first one is dark fantasy with rather nice and fitting story and ending, the second one is set in mystical Japan, the third one is set in dystopian future.