Maybe it's a personal thing, but I always felt that swimming and alligators were mutually exclusive!

I'd start with Redrum's excellent suggestions. I'd add an airboat ride through the 'glades. For camping, check Kampgrounds Of America. They are usually well priced with good amenities. I'll bet that their Florida cabins have AC. You'll probably want to book cabins early though (and not all sites have cabins)