YOW!!
Ya'll like to spend money! Biltmore, Grove Park, Bohemian. Sheesh.. No wonder this crew runs autogas. No cash left after dinner and a room!
But seriously, for a bucket list trip, the Biltmore and Grove Park are top notch.
The NC Arboretum is also good but if you do Biltmore, those gardens will fill the bill.
There are multiple places to go tubing.
Somebody mentioned mexican in an earlier post but could not recall the name. I imagine it was "Papas and Beer". Its good tex/mex and the portions can't be believed.
There is music nearly every night at Jack of the Wood (restaurant already mentioned).
If you drive SOUTH on the parkway (not towards Mt Mitchell) you can come to the Pisgah Inn. It has a restaurant with an outstanding view and good chow that is reasonable price. Pisgah is nearly as tall as Mitchell.
Walking downtown is well worth it in the summer. There are plenty of shops. Nicknacks, books, beer, beads, crafts, chocolate, crafts, food, crafts, music, and more beer. Go into Mast General Store.
SO... My favorite spot is Tupelo Honey. Downtown, just off Patton.