I'm not going to post a ton of recommendations. There are many good RPGs on PSP as well as emulators for older systems that have great RPGs that will work on a PSP. Google 'em.
However, I will share a tip for anyone interested in handheld RPG gaming. If you buy an Nvidia Shield tablet, get some form of bluetooth controller (i.e. an IPEGA controller) that physically attaches to the tablet, you will essentially have an 8" 1080p handheld device. Compared that to the 5" 720p screen of the PSP and it's no comparison.
The Shield can emulate PSP, Nintendo DS, PS1 and many more. Tons of RPGs to say the least. Add to that the fact that you can stream games from PC, buy games with the Nvidia store stuff and even play a bunch of dope RPGs on Android (and there are several, believe it), you essentialy have the most pimp handheld gaming device ever.
Did I mention you can use the Shield in Console Mode, hooked up to a TV? Use your spare TV as a Shield Console TV with another (or the same) bluetooth controller.
It's nice, it's real nice.