If you don't mind to possibly get your feet wet, this is the nature park for you. 
The address is: 3980 Corkscrew Road (also known as Gate 5). Open from sunrise to sunset. No fee - donations accepted. Dogs permitted!
The preserve offers about 6 miles of well-marked loop trails thru pine flatwoods, oak hammocks, wet prairie, popash slough, and two beautiful cypress domes. The trails are flat grass/sand and seasonally wet in low spots. 
Pick up a trail map at the entrance. The Wild Coffee Trail is especially beautiful. Be preared to encounter wild life. The adjacent Caracara Prairie Preserve offer a 2.5 mile loop across cattle-strewn pastures, beneath shady canopies of cabbage palm forests, and oak hammocks. Sweeping views of freshwater marshes dotted with wildflowers will also await you. 
Dogs are not permitted here for the safety of the cattle and nesting wildlife!