When we drive that route (we winter in Orlando and have kids to visit in Indy) some of our overnights that we like are:
Oak and Pines, Lake City, FL
Eagles Roost, Lake Park, GA
Twin Oaks, Elko, GA [one of our all time favorites]
KOA, Cartersville, GA [not really a favorite, but really convenient]
KOA, Sweetwater, TN
KOA, Corbin, KY
Whispering Hills, Georgetown, KY
These are not necessarily great campgrounds for longer stays, but, for us, good overnight stops on the route you talk about. They are all easy off/easy on the highway with pull thrus and full hook ups.
In case you do not know of it RV Park Reviews :: Home
is a great source for campground info.