Tombigbee SP has some nice camping. The sites surround a small lake, and there are ample trees. It's a relatively small park, but nice and quiet.
Take a short walk along Bear Creek (over the cable suspension bridge) if you stay there. There are some neat bluffs along the way.
“I think that when the lies are all told and forgot the truth will be there yet. It dont move about from place to place and it dont change from time to time. You cant corrupt it any more than you can salt salt.” - Cormac McCarthy