The BRP just north of Bedford, VA is quite nice riding. A worthy diversion is Rt 60 towards Forks of Buffalo. It takes about 30 minutes to zip down the mountain and back up to the parkway. Another diversion is rt 130 (near Big Island, Va) to US rt 501/130 to Glasgow, VA. Stay on rt130 to I-81S (just a few miles) then exit Buchanan and rt 43. It's a roller coaster ride back up to the BRP. Continuing south on the BRP into Floyd County, Va are enough diversions to keep you busy for a week of riding. But, the parkway is nice thru there. Tuggles Gap (rt 8, near Floyd, Va) has a nice little motel and good restaurant (try the Tuggles Gap pie) and they serve beer! If you are there on a Friday night, it's worth a trip to the Floyd Country Store
http://www.floydcountrystore.com/ While stopped at Tuggle's Gap, if you take Rt 8 towards Woolwine..the road winds down the mountain alongside a stream and is a real challenge to ride quickly. From Tuggle's Gap to the bottom and back takes about 20 minutes.
About an hour south of Tuggle's Gap, you'll pass one of the most photographed stops on the parkway...Mabry's Mill (restaurant should be open att).
Continuing south, there's a nice motorcycle campground (with cabins) at the Meadows of Dan exit.
http://www.willvillebikecamp.com/While in that area, Squirrel Spur road is a wild ride and worth your time.
There are many, many other great roads that intersect the parkway in VA and NC.
BTW, gas can be scarce while riding the BRP so plan accordingly. I keep in my tankbag-a list of exits on the BRP that have fuel.
Good luck!