If "Ohio47" means you're from Ohio - perhaps southern or southeastern Ohio? - and neither of these two hikes work out for you, another place to consider, not too much further east, is the Mt. Rogers area, near Damascus VA - may be about the same drive, is not overly rugged, and has a herd of ponies as a diversion. Very pretty area, fun to hike.
Didn't pull out a road map, but that may put you even closer than if you lived in Ohio. Not trying to talk you out of your original two ideas, just offer a third option in case neither of them works out.
Loc: Washington State, King County
Just to locate these options a little better, Carvers Gap is around NOBO mile 374 from which you're talking about going north about 14 miles, and Watauga Lake is around mile 424 (these are both relative to Springer Mountain), and your second option is to walk south to that from where rte 91 crosses the AT at around NOBO mile 442.
Going north from Carver's Gap has some ups and downs, and can be windy on the balds there --- though I hiked that in late March last year when it was pretty cold out still. The Overmountain shelter is moderately cool as a converted barn (was quite "cool" when I was there --- lots of large gaps in the walls of that barn).
From my recollection, I think you'll find the shorter distance more hilly/climbing, but perhaps a bit more scenic with the balds in there, whereas the Watauga lake stretch you're considering might be a bit better/easier trail overall. In general I wouldn't think that water or shelters would be a problem.
Caveat: I've only been through there the once; pay more attention to anyone who has a more frequent/intimate knowledge of that area.
I went through Damascus while riding a stretch of the Virginia creeper trail. Its a beautiful area, and the creeper trail runs with the AT for part of the trip too. As a result I've never hiked any of the AT, but I have biked a little of it :P. That, along with a trip to Fall creek falls is what got me and my girlfriend interested in taking up hiking. I cant speak for the other areas being talked about, but Damascus was pretty nice.
Loc: north carolina
Carver's Gap to 19E is a much better hike. Better views, better payoff for the climbs. The open balds are fantastic. Take your time and soak in the views, no need to hurry. This is one of the top hiking destinations in the Southeast.
There are numerous places to camp. I like tenting near the Overmountain Shelter (a.k.a "The Barn.") Great views as dusk falls, plus there is a fairly reliable spring.
The trail south of TN 91 is fine, it's a lower-elevation ridgeline walk, but there will be no views when the leave are on the trees.