You will find plenty of trees. Great place for a hang, do enjoy.
Scars are tattoos with better stories.
I did a week with Konnarock Crew last summer for the brier ridge rehab and found a spot about two tenths of a mile N of Thomas Knob at a large group camping area right on trail.
This is near where you will be staying the first night, BUT I WOULD highly recommend continuing North on the AT till you get to top of a couple of hills. Then, when you come to the last hill about a half mile shy of the area i mentioned above, the AT will deviate directly left. Proceed straight down the mountain thru the field to an oasis of open friendly hanging spots, as well as sites that have wind cover. This is the southern side of Rhododendron Gap--the water at the fenced spring is tasty and reliable, and there are plenty campsites all around. That area really is a playground--you could set up camp right there and spend days exploring all the nooks and crannies of Wilburn Ridge.
The beginning of the Pine Ridge trail will have few campsites, but past the first spring (which is about halfway along) it becomes more wooded and there are nice sites on the right side of the trail a tenth/half mile past the spring.
You will also have the power of the hammock, so you wont have to set up at conventional sites should the circumstances catch you such as weather--to which you'll want a natural wind block, drop elevation for lighting, OR the worst circumstance--CROWDS.
Best bet is to get that great Nat. Geo. map of the whole recreation area. There are so many more trail miles there besides the AT, and some of them have even better scenery. One could camp for two weeks up there and not cover all the trail it has to offer.
Have a great trip!! Feel free to PM for some "secret" campsites or any more questions
safest place to leave a car is grayson highlands state park's backpackers lot in Massey Gap. puts you right up close to the crest zone too