WOW there are about 200 caves in my area (Austin) alone. Ive been to Carlsbad in NM and Devils Den in Ark and a few others in the south. Those places are great and all but very touristy. Whirlpool cave has to be my favorite with its corkscrew entrance and its birthing canal (I havnt made it through the canal YET!). A lot of these caves are locked up but are accesible if you get a hold of the right people. Here is a link to some training our group has done in Whirlpool.
Ive been told Airmans cave also here in Austin is the 7th longest in the states.
http://keyetv.com/local/local_story_230212737.html