Fantastic audio tour of Biltmore House just an hour away from Hot Springs, NC makes this a perfect way to spend an afternoon. Also, skip the small cafes and cafeteria style dining options and head right over to the Deerpark Restaurant for a fabulous, upscale all you can eat buffet for $17 pp for lunch. It was a perfect day--of history, architecture and fine dining.
The Max Patch Trailhead is a great place to see the mountains. The open pasture on the mountaintop offers a clear view. The drive is a bit of an exercise, on winding dirt roads, but the view is worth it. Several Hot Springs locals recommeded it and Max Patch is worth the trip. Ask locals how to get their, or stop in the National Forest office in Hot Springs for directions.