Start by taking one of the local bus tours. We used Gray Line and were very impressed, enough to do it twice. The history of the town is quite fascinating, especially concerning its history as a medical resort and the art deco history of downtown (one of two noted art-deco centers in the nation).
See what is showing at the Folk Art Center, it might be interesting. The region is very craft oriented, as a result of a government initiative to stimulate local commerce during WWII. I spent two hours in the Folk Art Center being fascinated by a quilting exhibit (which I never, ever would have believed beforehand!).
For an interesting drive, go to Marion and then take 226 and 226A up to Little Switzerland. Little Switzerland is just a wide spot in the road, but seeing the little mountain cabin and retreats on 226A is worth the entire trip. On a side note, I would not recommend a large car for small mountain roads. Driving was taxing until I traded our Charger for a Focus.
I also second the earlier suggestion of Lake Lure, plus the various little towns and their weekend festivals. We also enjoyed Asheville's Botanical Gardens, and Lindville Gorge (out of town).
