Allstays lists a South Oaks Mobile Home and RV Park in Palmetto. It's fairly close to Fairburn. I have never stayed there and can't find out a whole lot about it on line. In fact, I drive that section of I85 fairly often and have never even seen the place advertised. Sounds like a ringing endorsement, doesn't it?
It might be fine, but you might want to check on it a little more...
There are just not many campgrounds close to the city.