Last week's podcast over on the Ultima Codex covered options for getting the games running on various mobile platforms. It's a pretty long episode, but it along with the short-version show notes can be found
here.
Ultimas VII and VIII (including Serpent Isle) would probably be the easiest to play using solely touch controls, as they're mouse-driven engines in the first place (although I don't remember how much right-clicking and such ended up being necessary, it's been a while since I've played any of those), but Ultima VI and the Worlds of Ultima games come pretty close, as movement and action controls all have on-screen buttons to do that with, too - the only thing you'd have to consider is conversations.