I'd say Lunar: Silver Star Story or even better, Final Fantasy IV with subtitles. Nothing will be missed and the stories are written well. In KRPGs, I'd say Epic Hearts.
As a RPG addict who never plays games with the sound on I have yet to find an iOS RPG release that requires sound so don't feel you're limited on the basis of being deaf. I can not think of a iOS RPG that does not have subtitles (but maybe there's an odd one or two that is voice only?). Some general recommendations are Fall of Angels (JRPG), Partia (strategyRPG), and CrimsonHearts (action/KRPG).
Lol... that would exactly be my other recommendations. But it's correct, most iOS RPGs can be played silent. Oh btw., try the FREE games Undercroft and Tunnel Tails! Both worth playing and fine without sound. And if you're into adventures too, try the Baphomet's Curse ports or Ghost Trick.
The Quest Couldn't let a thread like this go by without nominating The Quest (lite) (Gold) I particularly wanted to mention this one because it has decent story, plenty to read, and a very interesting/intertwined quest system. Also, there's a decent amount of visual feedback as to how the game should sound/feel. If you do try it out, here's a big tip - don't leave town until you've spoken to everybody and gotten an idea of what's going on - don't run straight out of town and get slaughtered immediately! The game features a very open world and is perfectly happy to let you wander into situations you might not be ready for...
+1; If you download The Quest Gold (and any number of it's insane but still constantly growing amount of expansion app content) it's possible your life will never be the same again.
Fall of Angels is one of the best iOS original RPGs. I highly recommend it. It's got a compelling plot and some novel puzzle designs with turn based japanese RPG combat, good world exploration. The art design is at times wooden but it's great gameplay wise. Well worth the $3.99. There is a free lite edition to try or you can read more positive comments from the Touch Arcade community in the Fall of Angels thread.
In Fall of Angels you do level up and earn skills; skills are also earned by plot development were certain locations trigger new abilities. For some unknown reason appshopper indicates the lite was removed.
LSSS & FFIV are two i recently got and are both amazing. But I agree, any iOS RPG should be playable without sound.
I also agree with this. In fact I'm not sure that any of many the games I've currently got on my iPad or iPhone require sound - some benefit from it but I can't think of any that require it.