Are you looking for a wilderness setting or just camping in general that is not a state park? If you are just looking for somewhere to pitch a tent, I used to camp at Lake Hogan (Twin Bridges) in Gwinnett before autox's. Owner is really cool and you can get all drunk and fish or walk around the lake. I like Fort Yargo also, but I am sure it will be really crowded (need reservations). Chattanooga has the Cherokee State Forest, which you could easily lose the crowds in considering how large that place is (no reservations). There is also the camp grounds around Lake Hartwell right on the border of SC and Ga (need reservations). I will most likely be camping in Panthertown, N.C. this weekend before a big climb at Laurel Knob.
Head up north to dahlongea or over into NC / TN in the smokies. Lots of back country camping up there.