Actually the BRP is a pretty easy drive. Only the tunnels would give any problems. The roads leading to, and from it are worse than the BRP itself. Do not try to tow up, or down highway 80 to Marion. 226 is also a bad idea. 221 is only steep, and twisty near the top. We tow our 30' TT on the BRP from Linville to Glendale Springs, and would not hesitate to tow any part of the Parkway. We have been camping the BRP for more than 30 years. You will also find picnic areas scattered out along the BRP with picnic tables, and rest rooms. Usually close to the CGs.
The NP CGs on the BRP are pretty nice, but primitive. However they are VERY quiet. they are also cool, even in the summer. You don't need AC to sleep well at night. You may need a blanket though. All have dump stations.
enjoy the Parkway, and take your time. Also don't try to take your 5er in to Blowing Rock. Just not room.
To do the entire BRP. give yourself at least a week. So much to see, and do. From where it ends in Cherokee NC, to Va. It does not go into Tenn.
There are a few private CGs with full hookup on, or just off the parkway. Bear Den, near Little Switzerland, Raccoone Holler, at Glendale Springs, and Miller Camp, near Laurel Springs.
I do agree. Run Cg to CG, unhook and then go enjoy the overlooks