North Carolina has been working on the Mountains to the Sea trail for a while, so that would probably be my first choice, even though they started work shortly after I left the state.
When you hit the Blue Ridge Parkway, I'd head up to Boone and then work my way over to Damascus, although U.S. 421 from the U.S. 321 turnoff up to the state line might be a bit sketchy. I suppose you could take 321 to Elizabethton, TN, and then go up through Shady Valley. Beautiful terrain up that way, paralleling the AT going north, but 321 is winding, although lightly traveled. 421 gets the most traffic, and it's maybe even worse for winding over Iron Mountain. 421 is downhill coming out of Boone to 321, and downhill from the state line to Mountain City. If I could arrange to hit that stretch on a week day, I might be tempted to brave the shoulderless uphill stretch to the state line, then cut through Laurel Bloomery to Damascus. The stretch right around the Virginia/Tennessee state line has so many curves that traffic is pretty slow, though not too light, and you'd be following the creek down, so there shouldn't be too much of a speed differential.
Unfortunately, I can't tell you anything about the North Line route on the link Jennifer sent. I'm curious where you'd cross into Virginia or Tennessee on that route. I'm guessing you could ride north into Grayson Highlands, and pick up U.S. 58 for the thrilling ride into Damascus. Alternately, it might take you through Pottstown to 421 at Trade (the state line).