I highly recommend 12 Bones in the River Arts District if you're looking for pig. They do it right. If you're looking for an interesting culinary experience check out Zambra on W. Walnut St, excellent Tapas and lots of good wine/spirits (though their beer selection sucks). Very cool atmosphere too with live jazz on Friday and Saturday nights.
My wife and I hit Oskar Blues Brewery in Brevard (~40 minutes from Asheville) after hiking the other day and it was fantastic! Got a private tour from the head brewer and tasted all their beers. Definitely worth it if you have the time.
I also highly recommend The Thirsty Monk, my personal favorite beer bar in town. Excellent selection of American craft beers and a huge supply of authentic Belgians.
Other places worth visiting if you have time: Mela (Indian cuisine), Wicked Weed Brewery, Highland Brewing, Pisgah Brewing (Black Mountain), Nine Mile (Carribean-inspired cuisine and nice selection of craft brews), Isis (in West Asheville; 23 beers on tap, good food), Jack-of-the-Wood (Greenman beers)., and The Bywater (laid back bar on the river w/ grills and live music.)
Have fun in town! Cheers