I recently did the section from the trailhead at Fox Creek on VA 603. This is just north of the Grayson Highlands and is about 42 miles out of Damascus. You can park there at the trailhead. But, it also depends on what time of the year you are thinking about hiking. Right now in this area it is cold and wet. There will probably be a good bit of snow up in the Highlands and down to about the 2500 ft level. This is a very nice hike in good weather, but each year someone gets in trouble in the winter.
You can also go south to the Lake Watauga trailhead and hike about the same distance north to Damascus. Not as pretty as the hike from the north back to Damascus but the conditions will probably be a good bit better. Both hikes are pretty mellow so you can make good time if the weather is ok.
You can call the Mount Rogers Outfitters or Sundog Outfitters and they can give you real good info.
Waterboy 99
Waterboy 99