There are many Atelier games on Vita, but Atelier Ayesha Plus: The Alchemist of Dusk is probably the best starting point. Not only does the enhanced PS3 port look great on Vita, it has a tremendous amount of content, and a really enjoyable turn-based combat system. That's all on top of the series' signature crafting system.
Fans of strategy RPGs can't do better than NIS America's Disgaea series. Enhanced ports of the third and fourth titles are on the system, and while both are worth buying, we'd give a slight edge to Disgaea 4: A Promise Revisited. Not only does the game feature a hilarious story that'll teach you a lot about sardines, it also features a bunch of new features from Disgaea D2. If you want to see all the game has to offer then it'll be the only RPG you'll have to buy for a while.
Final Fantasy X was a great game on PlayStation 2, and it's still highly enjoyable on Vita. In fact, the added bonus of being able to play Square Enix's turn-based RPG on the go is one of the best perks of this version. Whether you've played it before or not, it's worth picking up.
Monocrhome Corporation's Grand Kingdom is one of the most unique tactical RPGs. Combat takes place in several lanes, and players must carefully arrange their units if they hope to succeed. There's also an in-depth online component that gives the game legs.
If there's one RPG that every Vita owners should play it's Persona 4 Golden. It's not often that I genuinely care about every member of a large cast of characters, but all of the P4 characters hold a special place in my heart. Not only is the gameplay phenomenal, it's also one of the most satisfying gaming stories in recent memory.
The Shiren The Wanderer franchise is legendary to dungeon crawling fans, and The Tower of Fortune and the Dice of Fate is a good showing of why the series is so beloved. The RPG can be downright cruel and unfair at times, but there's a great satisfaction that comes from beating the odds and finishing a tough level.
While Monster Hunter moved onto the 3DS, PlayStation Vita owners still got some great games in that vein. One of the best ones is Sony and Marvelous AQL's Soul Sacrifice Delta. Directed by Teruhiro Shimokawa, the action RPG features some great art design, satisfying combat, and plenty of content to keep players busy. It also features online play, which makes it one of the best co-op experiences on Vita.
The most recently released addition to the list, The Caligula Effect is a dark role-playing game that takes place within a virtual world. It deals with a lot of adult subject matter, and is some of Tadashi Satomi's best work. It has a slow start, but the payoff is definitely worth it.
Both of the The Legend of Heroes: Trails of Cold Steel games are worth playing. While the sequel doesn't add a ton in terms of new features, the fantastic turn-based combat is just as satisfying the second time around. The sequel also delves into the lore of the world, so it's not a series to be played out of order.
Those looking for a good action RPG will find themselves pleased with Ys: Memories of Celceta. It may not feature the greatest plot in the series, but the combat is top-notch, and there's an exciting world to explore.