Lisa- my favorites are all mostly in the Raleigh/Durham/Chapel Hill area. I have been thru Asheville many times but have not really gone to the nurseries there. I know there are many and i am certain they are great :-). that being said- these are my favs:
Niche Gardens- natives and lots of other perennials- cool gardesn to walk around in, open all year, nice catalog.
Big Bloomers- Sanford NC- the biggest trip from the Raleigh area, but worth it if you are a salvia / unique plant nut. They do get a few proven winners in, but most of their stuff they propagate themselves. plants are smallish but most are under 5 bucks. has annuals too- although on the NC zone/timeline, not in sync with our climes. no catalog, and not much online- kind of a word of mouth sort of place- folks come from all over :-)
Plant Delights- i suspect everyone knows about pdn :-). Big, healthy, and pricey plants- but most are worth it. doesn't carry too much run of the mill nursery stuff. He is into research big time. They have extensive planted gardens that i believe you can walk around all year if you let them know you are coming- they sell online only with 4 open house dates per year. the next one are the weekend of July 7th, and the weekend of July 14th- so if nothing else i would go for the gardens
Catalog and extensive online listings
Camelia Forest is a pretty dedicated garden- mostly Camelias.
only open to public on Saturdays IIRC. I didn't make it my last trip- my blazer was full lol. worth it if you like the things they carry. they do have a catalog, which is good, and they do online selling mostly. some full weekends open, but none in high summer- just the Saturdays.
links:
http://www.nichegardens.com/
http://www.bigbloomersflowerfa...
https://www.plantdelights.com/
http://www.camforest.com/
enjoy your trip- and hope you can get to Raleigh area- it is a bit of a hike from Asheville. IIRC 3 hours or better.