I enjoy James Island County Park when staying near Charleston SC. I don't know if you travel with pets, but they have an awesome dog park. Great bike trails, too.
My favorite in Nashville is Seven Points, a COE campground on Percy Priest Lake, east side of the city. No FHU, but if you didn't camp there it's still a nice visit. Very close to I-40. Matter of fact I'll be there ten days from now on my way SE.
About a half hour NW of Atlanta is Lake Allatoona, a COE area that's very nice. I think they have 8 campgrounds near the lake. I love McKinney. It's close to I-75 and has 150 sites. I don't believe they have FHU, either, though.