Dear jsl,
I've been meaning to answer you in some detail but haven't gotten around to it. I live in NC in the very NW corner. 2 miles from TN and 5 miles from VA. We are very near the BRP as well as the Appalachian Trail, Mount Rogers, Boone, Grandfather Mountain, etc. I'm sort of familiar with a lot of the Parkway especially the parts around here.
A great multi-day trip would be to do the Skyline Drive through Shenandoah Valley area (our least visited National Park), then hook up to the BRP and continue all the way to the Smokies (our most crowded National Park).
What do guys like to do? Hike? Fish? Canoe? Bike? Collect waterfalls? Drink copiously? Rough camping or do you need hookups?
When? Remember these mountains can be interesting weather-wise. Night before last we hit minus 14 (with 55 mph gusts). Winter can last into May some years. Spring is nice. Summer is awesome. Fall is a religious experience. For us Oct 1-14 is usually peak leaf season.
We have a 120 acre farm and you are certainly welcome to stop here and camp in the driveway or up in the upper meadow. It's almost undoubtedly more beautiful and secluded than any campground you will visit.
In fact, for anybody reading this, we are interested in finding anybody that would be interested in house/pet sitting for us. We'd love to be able to take off for a month or more, but it's been tough to find folks to stay here. We're not in a position to really pay more than expenses, but this could be a great place to base camp from for all the activities listed above and much more.
O.K. When I s aid "anybody", I'm obviously looking for somebody responsible and mature. That leaves you out Frank.