If you have a little time, there are several small towns around the area that are neat side trips.
Hendersonville
Flat Rock
Brevard
Tryon
Sylva

Down towards Hendersonville, there are several wineries, Burnt Shirt Vineyards is a favorite.
https://www.burntshirtvineyards.com/

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.

https://thegorgezipline.com/

Less than an hour south of Asheville:

http://www.nctubing.com/

Or in Asheville:
http://www.frenchbroadoutfitters.com/

An hour away is Greenville SC. (My home) Lots of restaurants, shopping, and outdoor adventures.

http://www.visitgreenvillesc.com/

Come tour the BMW factory, or take the BMW driving course.

https://bmwperformancecenter.com/

If you go into the National Forest, check out Sliding Rock...

http://www.ncwaterfalls.com/sliding_rock1.htm

If you come in the late summer to fall, there are several orchards within an hour to pick your own apples and enjoy local jams, jellies, honey, and baked treats....

This one is on top of a mountain near Hendersonville:

http://www.skytoporchard.com/

They make fresh apple cider donuts with powdered sugar and cinnamon. They are to die for....