I’ve gone to several of the big ones in the East like Luray and Howe Caverns. Those were big and led by guides and quite easy.
In Costa Rica, we went into a small cave with a guide on a muddy day. There was some wading through water in the beginning and a place where you could take a very narrow path or a slightly wider one. My boys did the scarier one and I did the wider one but it was still a small cave.
In France, I’ve been inside several that had cave paintings on the walls. The one at Niaux (sp?) was particularly impressive – we walked about 800 meters along and then the guide shone his flashlight on the walls in the large chamber.
I’ve also done rock scrambling and slithered up the Lemon Squeeze at Mohonk Mountain House in New Paltz, New York.