I've camped several times in the Southern Appalachians. Beautiful country, heavily wooded, creeks and waterfalls everywhere, one of the most biodiverse regions on earth outside the tropics. Where dispersed campsites exist, they are often hacked out of the woods along back roads and remain clear by continual use. Enforcement is generally lax away from the big tourist areas, and many of the campsites are trashed by partiers and hunters. Many others are slightly overgrown, tucked many yards away from the road down a rutted path, perfect for peace and seclusion. Some official primitive campsites don't require any fee, just a sign-in.
If you are accustomed to Western lands, you must realize that Eastern national forests are a patchwork quilt of private inholdings and forest land. Most of the private land is posted, and the owners live on their land and do not take kindly to trespassers. To find public land, use this official map (
http://www.fs.fed.us/locatormap/) and zoom in on the forest of choice. The outline indicates the "declaration area". Light green is private, dark green is public land. Also, stop in the local office and get a MVUM (Motor Vehicle Use Map). These free maps show all of the public roads in the national forests, helping to avoid frustration when you pass road after road closed off with locked gates and posted against vehicles.
Solar would only be good for a couple hours a day in wooded areas. If you are able to find a high mountain bald that allows camping and vehicle access, you will get pristine mountain spring water, a kick-ass view, plenty of wildflowers in the spring, plenty of sunlight on sunny days, and cool summer temperatures. The Wikipedia article on balds has a list of mountains with bald tops. Check them out on Google Maps for roads, then visit your USFS office to determine camping restrictions.
The Blue Ridge Parkway traverses some of the most spectacular mountains outside the Smokies, which are a national park and off-limits to camping. Camping along the Parkway itself is illegal, there are often steep inclines and drop-offs along it, and the number of connector roads are limited. However, the NPS corridor along the Parkway is very narrow in spots, and you just might be able to find that perfect campsite on USFS land a stone's throw from the parkway, either along a connector road, or any reasonably level spot where you can squeeze your rig out of sight of the road.
There are plenty of less spectacular spots miles from the nearest highway where rangers are as rare as hen's teeth. Talking about teeth, a lot of the local residents don't have many of them left. Don't let it scare you, unless you were snooping around in their moonshine operation.
Enjoy your time in the Eastern hills.