I've hiked into Hot Springs twice on the AT from the south. Max Patch is a short drive out of town. From there you could hike north to Roaring Fork shelter (good water). Walnut Mountain is a steep climb just north of Roaring Fork and despite what trail maps indicate, the water there is better suited for mosquitoes (big ones). There is good water about a half mile before the shelter.
If you go north out of town it is a good climb (actually out of Hot Springs its a climb in both directions). You will walk along Lovers Leap Ridge. About 7 1/2 miles out of town you will come across Round Top Ridge Trail. Its the old AT route. It will lead back to HS (8 miles). I have not hiked this trail so I'm not sure of the condition.
Friends that have hiked this area recently have said water is not pentiful. Check with the guys at Bluff Mountain Outfitters. They are familar with trail conditions and will be glad to make suggestions. They also do suttles.
Hope this helps!