Little Switzerland Inn is a nice spot to base out of, or spend the night. From Little Switzerland, you can go to Grandfather Mountain, which is a pretty nice ride. They filmed part of Forrest Gump, where hanks was running up a mountain, on that mountain.
Be sure to go atop Mt. Mitchell. IIRC, it's the tallest spot this side of the Mississippi. There's a restaurant up there, altho I haven't tried it. From my old Wing forum days, there was a rider who requested his ashes be spread out atop that mountain, of which a few fellas did for him. So you may hear some spirits whispering at you. Last time I was there, there was fog rolling across that mountain top, which was pretty kewl.