It depends on what you are looking for, really.
Thirsty Monk is rated one of the best beer bars in America. Upstairs they have about 30 taps with american style ales, downstairs is Belgian beer theme. It is most certainly a must.
You really want to check out the south slope of downtown, aka "the brewery district". Here you will find 6 breweries within a couple blocks of one another. Literally, all of the south slope is NOTHING but breweries. I would recommend hitting up Wicked Weed if you get hungry. They make some great brews and serve up some pretty nice food. If pizza is more your thing, try Asheville Brewing and Pizza, they just won gold at the World Beer Cup for their Ninja Porter.
If you have an evening dedicated to it, you can take the Asheville Brews Cruise. You can check out the details
here.
Hopefully this is helpful, but if you have questions feel free to send a PM.
cheers!