Not to take anything away from Klattu's first suggestion, we have found all of the Florida State Parks to be excellent destinations. There is Fort Desoto County Park near St. Pete, Fort Wilderness at DisneyWorld is awesome.
Closer to you is the Okefenoki Swamp. But really, the best recommendation was alansd's recommendation to join the Springstream thing in North Georgia.
2008 Airstream 27FB International Ocean Breeze
2014 Ford F250 King Ranch 4X4 w/6.7L Diesel, Hensley Hitch