My Personal Recommendations:
Fairchild Tropical Gardens: A unique experience for North America. It is about as complete of a 'tropical' garden as you can get in North America.
Everglades National Park: The largest subtropical wilderness in the United States, Everglades National Park protects an unparalleled landscape filled with curious flora and fauna. At nearly 1.5 million acres in size, the park provides important habitat for numerous rare and endangered species like the manatee, American crocodile, and the elusive Florida panther.