there is more than one mime and there are at least 4 materia caves if i remember. there is one south and slightly east of wutai on black land that you cant land your air ship on so you need a green chocobo or better. there is one at the end of a chain of islands to the south in the mideel area but you will need a blue chocobo or better, once again it is on black land so you cant land your airship there. and im quite sure there is one in a patch of desert with a mountain cave which youll need a black chocobo for. this square of desert is very near the cave with the old man who gives you mithril i think (i think you need a black chocobo but you might not need so high a level chocobo.) and the final materia cave is on round island to the north-east very near the corner of the map. there are two mime materias, one quadra magic materia and of course the knights of the round materia.