Welcome to the Dis!
We travel along that route, and we usually stop at one of the Flying J truck stops for the night. We stopped at Amy's South Georgia RV Park this last trip and it was fine. It is further south than you may want, though. It was in Tifton--(mm 60). We had planned to stop at the KOA in Forsyth (somewhere between 180 and 185) on the way back this last trip, but the kid was sleeping so we sailed on past and stopped at the Flying J at mm 201 and slept there. I haven't ever stopped at this KOA so I can't really offer a recommendation.
I don't know what your camping vehicle is so I don't know if a truck stop will work for you, but they often work for us.
Have fun planning!! When are you going in June? We'll be home at FW again in late June through the 5th of July!!! I can't wait!!!