Yup. Mythrill Mines is my personal choice for building limits as well. I try to get everyone up to at least the first level three limit before leaving.

I always dismissed Aeris' Limit Breaks due to her impending death although... I think on my next playthrough I'll get them built up... just so I can see what Great Gospel is like.

Actually, how is that possible? I've always had the highwind when getting to the sleeping man in the cave. How can you get the piece of mythrill off the guy before Aeris snuffs it?