I can't give you a rec on an RV rental, but I just wanted to chime in on our Georgia State Parks. They are beautiful and you can probably find something to fit your style within 1-2 hrs from Atlanta.
We also like to go up to Lake Allatoona, to McKinney COE(Corps of Engineers) campground. It is woodsy and on the lake. There is a swimming beach and clean bathhouses. Not a lot of planned activities inside the park, but Red Top Mountain State park is only about 5 miles from McKinney.
Another campground we love is a Trackrock Campground, up in Blairsville. I live in Marietta and we can get there in 2 hours. It's a private campground, has full hookups, playgrounds, swimming, hiking, horseback riding, and a hayride on Sat night. The owners have a lot of experience with RVs and will even help you set up, if you need help. And if you get bored you can run over to Brasstown bald or Helen for awhile. But you won't get bored at Trackrock.
