Big Cypress National Preserve: Alligators, hiking, humidity...Florida.
Castillo de San Marcos National Monument: The oldest masonry fortification in the continental US. Made from coquina shells.
Dry Tortugas National Park: A few hours by boat off the coast of Key West. This is an impressive fort, especially considering everything, including water, had to be imported.
Everglades National Park: Like Big Cypress, this place has gators (without fences) and birds, and a trolley if you don't care to walk!
Fort Matanzas National Memorial: Basically the little brother to Castillo de San Marcos.