I’ve twice ridden the entire length of the Virginia Creeper Trail (https://www.traillink.com/trail/virginia-creeper-national-recreation-trail or http://www.vacreepertrail.com/index.html), which runs—mostly downhill—from Whitetop, which is on the Virginia/North Carolina border, to the biker-friendly town of Damascus VA. The trail continues from Damascus to Abingdon, Virginia.
I highly recommend the segment from Damascus to Abingdon. It seems like 95% of all riders stop in Damascus, so you’ll have that section of the trail to yourself for the most part. And, in my opinion, the second half of the trail is really beautiful, with much of the route through countryside farms and forestland.
As I noted above, I’ve ridden this trail twice—the first a solo ride, the second with a group of family friends. The pictures below are from my first ride; you’ll note that my old red Diamondback mountain bike figures prominently in several of the photos.