Anyways, after you get Edge in the Cave of Eblan for the first time, where is a good place to train? I am training because in the Babel Tower (Underworld) yesterday, I was struggling to get up there without being beaten (halfway) to death.

Just run the Babel Tower's first few bits and then exit to heal. If you really need to train, that's about where you do it. Training sort of kills JRPG's in general for me, though, so I don't do it much if at all. Keeps battles more fun, too.