Well, the OP is obviously long gone, but others may use this thread for suggestions

I would recommend a canoe trip down Peace River on the west coast. Camping is allowed, you can rent the canoes and be picked up at the far end. A great, relaxing trip! The only gators that are supported by the areas game are smaller, younger ones. And lots of otters playing in the water!

Another great suggestion are the springs near Gainesville - High Springs, Ginnie Springs, Poe Springs - the water is crystal clear and 65 degrees.

Ocala National Forest is beautiful, filled with trees and a great wandering spot.

In South Florida, I liked going to the smaller keys - not Key West or Islamorada, but the lesser keys to fish, swim, or just watch the ocean.

I'll second the recommendation for Morikami Museum - they have a wonderful location and huge Japanese gardens, as well as the tea house and bonsai trees.

On the west coast, Venice is a nice community with wonderfully white beaches - do they still have petrified sharks' teeth there scattered around?

Cedar Key is lovely - I was there last April during an art show, and the island is reached by driving through a hammock of many small islands and fen.