Asheville, NC: if you're going to hit up one brewery there it should be . . .
It depends on what you're looking for.
I liked New Belgium for the "scene." Great tour with good amount of free beer. Nice river views from the tasting room. Large outdoor lawn with food trucks to play on with your kids or dogs or significant other.
I liked Wicked Weed Funkatorium for the beers (almost all sours, if that's not your bag, this is not your place), though some would now object because they've been bought by AB-Inbev. I liked WW Funkatorium a lot more than their main Wicked Weed brewpub (which features their whole range of beers though only one or two sours at a time)....much more relaxed atmosphere at the Funkatorium.
And Burial for their hoppy beers, though they're probably not in the same league as the Veil (I didn't actually go there, but have had some of their beers.)
Pisgah Brewing over in Pisgah was fun if you're into watching open mic Grateful Dead cover bands and making fun of hippies (they also have a larger concert area featuring nationally touring bands, bookings tend toward the jammy.)
Some people rave about Sierra Nevada over in Mills River, but I found the atmosphere too sterile and palatial.
And Fonta Flora Brewing, in Morganton, which may or may not be on the drive to Asheville, was a very nice stop off place. Laid back vibe and excellent beers.