Too far to do the whole thing in the time you have, and you'd want to arrange safe parking and shuttle with one of the hostels.
That said, Sam's Gap to Hot Springs (N-S) is a 45 miler, climbing 8900' and descending 11200'. You'd end up in Hot Springs, where you could book a hot tub soak and a massage. There are one or two hostels in Hot Springs, and you could probably work out shuttle that way.
EDIT: Carver's Gap, on Roan Mtn, south to the Nolichucky River, is about 32 miles, climbing about 7200' and descending about 11,100'. Uncle Johnny's in Erwin, will do shuttle for a price. Start from 19E to add another 14 miles, but do NOT leave your car at 19E.
Iron Mountain Gap south to Sam's Gap is about 42 miles, climbing and descending about 11,200'. Again, Uncle Johnny's will get you from Sam's to the Nolichucky for a fee, and could get you to Iron Mtn Gap as well. You get ridge hiking, rhododendron, wooded areas, balds, the Nolichucky... I really like this section of trail.
All three sections obviously involve some ascending (nothing technical, just uphill), but each is lovely, relatively uncrowded, and has few problem bears. Water is plentiful and the topography is varied, with some excellent views here and there. I don't think you'd be disappointed by any of them, assuming the ascents don't put you off.