If you tijme it right, you can walk around in the crater (right before the end) and level up there. There is also a couple of rare materias floating around in the crater. So I would take the ariship to it, and follow the path, once you reach the part where everyone is standing, and you are deciding who takes which path, you can either take both paths, or just head back out to the airship. That spot is also a great place for the save sphere (you are given a portable one, that you can only use once.) Hope that helps a little bit
Oh and about your wonderful chocobo, they are only found in certain parts of the world, and the arena is NOT one of them. Each area gives you two different types of chocobos, so if you're not catching a wonderful, then you're not in the right area.
