A very interesting place with a nominal fee to visit is Blue Spring State Park. You would need to have access to a car to get there. The water in the spring is a constant 72 degrees and manatees come there as soon as the ocean water starts to get too cold for them. You can't swim with the manatees, but you can watch them and see the water bubbling up out of the spring. The park itself is pretty, with moss draped live oaks and a walkway along the water. (It's a refreshing break after milling around with the crowds in the theme parks.)
I could also recommend Leu Gardens in Orlando and the Morse Museum in Winter Park.