If you have a little time, there are several small towns around the area that are neat side trips.
Down towards Hendersonville, there are several wineries, Burnt Shirt Vineyards is a favorite.
South of Asheville is the small town of Saluda, which has a couple of great restaurants, and an authentic general store, right on Main Street. There is also a tubing and zipline adventure company in town.
Less than an hour south of Asheville:
Or in Asheville: