There are sections south of Orlando that feel like wilderness. KICCO, Kissimmee Prairie Preserve State Park, Big Cypress National Preserve. Then there is Lake Okeechobee Scenic Trail, basically a paved bicycle path.
Favorite sections are those I don't have to drive too far to get to (smile). I may be biased but I think I'm fortunate to live near the Aucilla Sinks, St. Marks, and Apalachicola National Forest, all with very much a wilderness feel. I guess true wilderness depends on one's definition. There are even sections of the Apalachicola National Forest with no cell phone reception! Bear in mind this is Florida, not Alaska or Montana where one might be expect to find areas out of cell phone range. The Suwannee section, not too far from me, is also very nice.