If you're into NASCAR at all, plan a stop in Charlotte. Fleetwood sponsers a great campground adjacent to Lowes Motor Speedway with full hookups and very reasonable rates on non racing weekends. Chck the Lowes Motor Speedway website for a link to the campground It's a good place to stop, even if you are not into racing. All of the NASCAR race teams have shops within a few miles and most allow visitors for free. The speedway offers tours for a reasonable fee-$5.00 if I remember correctly.
The Blue Ridge Parkway is an excellent choice. We traveled from Shenandoah to Balsam, NC on it last summer and enjoyed every bit of it. There are some spots that are steep or curvy, but we didn't have any problems in our 37 ft motor home. Just watch out for the overhanging trees that sometimes try to grab your roof! You won't make freeway speeds, but it's much more enjoyable.
In Atlanta, we have vowed to never stay at Stone Mountain Campground again. We have been twice and had lousy experiences both times. Most sites are old tent sites that they tried to convert to RV sites without spending any money. The staff was arrogant and not at all knowledgable. One time they put us in a site that had an 8 foot high red dirt bank six feet from our door, and it was impossible to get the rig level. The second time they checked us into a site with limbs down from a storm. When I complained, they said the only other place was to dry camp in the public beach parking lot for a day or two til they got it fixed. This at $36 per day! We left with a refund of the camping fee, but they refused to refund the $8 park entry fee that you have to pay to get in the park to register at the campground! However, Stone Mountain park is well worth the visit, with lots of history and entertainment. Just stay somewhere else. There's just not many choices around Atlanta for RVers. We decided to dry camp at a relative's home 40 miles away rather than stay at Stone Mountain Camground again.