Massie Gap to Mt. Rogers, 8 miles out and back is the obvious choice
Start at Massie Gap in Grayson Highlands State Park
Take the Rhododendron Gap trail to the AT
Take the AT/Wilburn Ridge trail to the Mt. Rogers spur trail (AT is easier/Wilburn Ridge is more scenic and difficult)
Here's a map. Massie Gap is at the bottom middle, (large image)
http://www.diybackyardworkshop.com/wp-content/uploads/2011/04/Map_GraysonHighlandsVA.jpg