Personally, I skip the little PITA ridge climb just past Watauga dam. Just stay on the road and in 0.3 take a left and the trial will be about 100 feet from the intersection.
Once the climb out of Watauga is out of the way, the rest of the way to Damascus is pretty easy. The exception is getting water, as it's usually located way down off the ridge or a long ways from the shelter. (which is also often the case through most of VA) Bring a big water bag, you don't want to do these trips twice!
The alternate water source for Vandeventer is 1.7 miles south of the shelter, but it's after most of the climbing is done. Water for Iron mountain Shelter is 0.3 miles south of the shelter, but on the trail. Water for the Abingdon Gap shelter is also a bit of a walk, 0.4 round trip. At least it's an easy walk. First time I did it I didn't pay much attention to the sign which said "WATER 1000 yrds". Took me a while to realize 1000 yards was a LONG way.