that little area there is truly the second-best portion of the entire AT (you can take my word for that).
Hot Springs and Damascus are both good towns to start out in, as the outfitters in both towns offer shuttle services to take you out there.
i'm not totally sure on a lot of the mileages because i don't have my Wingfoot on me right now, but either check yours or call one of the outfitters and they can tell you more about it.
there are three great areas around there that you can hike:
Max Patch: it's not too far from Hot Springs and you can take your car up there to a parking lot to start off (it's a bit rough, though). Max Patch is a georgeous 360-degree view. i think last time i hiked there to Hot Springs was a two- or three-day hike that wasn't all that strenuous since it was downhill most of the way into town.
Grayson Highlands: this is just over the Virginia border with Carolina and accessible from Damascus. rolling ups and downs with a lot of balds. the highlight there is the ferile ponies which are accustomed to people. take some carrots or something to feed them, but also hang up your shoes and such because they'll bite through your stuff at night for the salt content from your sweat.
Roan Mountain (my favourite of the bunch): if you start out from the parking lot at the top of the mountain and head north, you miss an awesome climb to the top that gets your heart going and also has a couple changes in forest coverage, which is neat. also the abandoned house. you get a flat summit walk for a little bit with some planks to walk on in the middle of a gorgeous little spot of pine trees. don't make the mistake of staying at the shelter on the top of the mountain, but keep going north for something like four more miles to get to Overmountain Shelter, which is a Revolutionary War era barn turned into hiker shelter and is a very well-known stop along the AT. very pretty little spot. not too far north of there and you start hitting more rolling balds. they're steeper than the Grayson ones. 360-degree views all around. granted, a winter hike over those if the wind is blowing can be rough. the wind can get pretty strong over those balds and it's just downright cold. there's a few rock outcroppings along the Trail that i ducked into to warm back up a little (that was kinda fun, though). so just be prepared if you choose that section. somewhere in the area there, there's a shelter run by B.P. nice guy and has a nice hostel. i don't think he does shuttles, but he might take you to town if your car is there.