Done some of these, haven't done others, but there are always non-touristy places worth exploring in Florida. | Huffington Post: These 12 Places Are Reason Enough To Head To Florida (Ichetucknee Springs pictured).
Pine Island, Florida, offers a swimming beach, swimming area, picnic tables, shelters, barbecue grills, observation point, volleyball court, playground and concession stand. Spring Hill, Florida, is located nearby. http://en.wikipedia.org