We've traveled all of the Blue Ridge Parkway with the various RV's we've owned, except the part with several low clearance tunnels
(less than 13'). All these are from mile marker 458 to 461 on the southern end in NC. We got off at US19 (when going south) to go around those. Everything in Virginia is no problem.
Grades in Virginia are generally less steep than in NC, but in both you will want to use lower gears to allow the engine to do some braking when going downhill.
We found we need to travel slower than the speed limit, especially around the curves, some of which are decreasing radius and very tight. With the larger MH we have now, it is not surprising to go 30MPH in the 45MPH zone, especially in some sections in NC. We pull over at most vistas to enjoy the view and let traffic go by.
Here is a webpage
that has a planned itinerary on the BRP with some notes.
On Skyline Drive in Shenandoah National Park, we've stayed both at Loft Mountain and Big Meadows and liked both, both offer hiking to waterfalls nearby. There are lots of ranger programs
to attend, be sure to check those out.
On the BRP (Blue Ridge Parkway), we have stayed at most of the campgrounds, even with our 34' rig we still can find a site that is level enough for use, though we sometimes have to use the "pull through" sites, some of which are really just wide spots in the campground road. Still OK for several nights camping.
IMHO, using a motorhome to drive the BRP is a great way to see the fall colors! Be prepared to go slow and stop a lot to see the vistas and other sights on the Parkway.