In the Big Bend region, Torreya State Park (outside of Tallahassee) for the hiking -- it's called the mountains of northwest Florida for a reason
In the Panhandle, Rocky Bayou State Park (in Niceville) for the trails and kayaking. If you're a camper this park has nice facilities and is just a short drive across the toll bridge into Destin if you want a quick trip into civilization for some great dining options