Okay, I did not play many, so I can't recommend a lot, but since you have Vita:
As DrunkOnEstus said, Danganronpa 1 and 2. The jist of the 1st one is that a bunch of kids got locked into a school with no access to the outside world. The bad guy tells them that they can either stay here forever or one of them kills someone else. In the case of the latter (which obviously happens), the death must be investigated and put on trial. If the killer is found out, s/he is punnished, if not, however, then everyone else is punished and the murdered can leave.
And just as DrunkOnEstus said, you won't enjoy the game if you aren't at the very least tolerant towards the common japanese tropes (MC who speaks about hope, dumb athlete, cool biker, etc.)
As for my own recommendation, I'd say Zero Escape: Virtues Last Reward. The plot is the following: 9 people are trapped in some kind of a bunker and must escape. Sorry, nothing more, spoilers. While it is not a straight up mystery game (i.e. you yourself do not look for clues, you only solve puzzle rooms and make ally/betray decision), the characters do slowly yet surely find out everything while searching through the bunker. The story is great.
And if you will find this game interesting, then wait for the release of an announced sequel. Also, again if you are interested, do check out the first game by the name of Zero Escape: 9 persons 9 doors 9 hours. Yes, it is was released for DS (or 3DS), but there are many ways to experience it, Let's Plays for example. and if you do like VLR, I recommend you to experience 999 just for the story sake. You can play VLR without playing 999 (like I did) and you will understand ABSOLUTELY everything, but there are things that connect those games.