Floyd/Roanoke area, Mile Post 120-190 region.
BLUE RIDGE PARKWAY Map 3 Part 1 From Milepost 106 (US 460) to Milepost 216.9 (The Virginia/North Carolina state line)
If you give me details on your point of origin, I can be more specific on the best route there.
The Parkway runs directly over Route 8, you'll want to get off and go South on 8. You will immediately pass Tuggles Gap Motel/Biker Bar on the left, and begin descending Woolwine Mountain. Go to the bottom, find a convenient place to turn around, and run it right back up to the top. Very low police presence, almost no houses. Confidentially, it's a very popular place for full-bore, unsanctioned race driving to the summit, whether on a bike or in a car. Multiple runs are possible. Traffic during the week is nearly non-existent, mostly log trucks. Weekends get more dicey as the area fills up with Hardley Abelsons aimlessly puttering about. VERY popular motorcycle route, as you'll see in the related video.
YouTube - Tuggles gap tard action