Two years ago I spent Thanksgiving at a Swamp in Georgia (actually a very nice house near a swamp). My friends lived near a State park near Valadosta GA and I woud just walk out into it every day (no boat though). Great place, everything is good in a Swamp.
Okeefenokee would prolly be ethe better bet. No hunting is allowed in there so you wouldn’t have to keep track of the Georgia hunting seasons to plan your trip.