Well, there's a good number of decent Japanese action/role-playing games if you don't mind a bit of grind in your games. Soul Sacrifice, Gravity Rush, Dragon's Crown, Muramasa: Rebirth, Disgaea 3 (and the first two from the PSP section of the PSN Store), Persona 3 Portable (download from PSN), Persona 4 Golden, just to name a few.
Soul Sacrifice is Monster Hunter-esque, but with a more fluid and action-y combat system.
Gravity Rush is an action-adventure game, with the same kind of structured upgrade system as something like Okami. It's got a bit gimmicky use of the Vita's motion controls and touchscreens, but most of those aren't required to play or progress through the game.
Dragon's Crown, you're probably aware of even if you don't already have it on the PS3. It's a side-scrolling brawler with leveling and inventory management. Pretty fun combat, absolutely beautiful in action in my opinion.
Muramasa: Rebirth was originally for the Wii, it's a 2D action-RPG made by the same guys who did Dragon's Crown. The combat system is better than DC in my opinion, and again, the art direction is absolutely fantastic.
Disgaea is a series of strategic-RPGs, like Final Fantasy Tactics or Tactics Ogre, or not entirely unlike XCOM: Enemy Unknown. Charming little story and it's nicely challenging, but probably involves the most grind out of any of the games on the list.
P3P and P4G are games that I can't recommend highly enough. They're really slow burners, though that's not unusual for JRPGs, but once they get going I've got no problem saying that they're some of the best JRPGs I've ever played.
BlazBlue: Continuum Shift EXTEND, a visual novel/fighting game that's a brilliant parody and love-letter to the insanity of a typical shounen manga series, with some of the most gloriously self-aware writing I've had the pleasure of seeing.
LittleBigPlanet Vita is pretty solid and fun as well, a 2.5D side-scrolling platformer narrated by Stephen Fry.
And if you're a fan of puzzle games, Zero Escape: Virtue's Last Reward is an especially challenging one built around the structure of a visual novel as well. It's got tons of different potential endings, too.