I'm in Saint Paul so have a slight bias, but I love Happy Gnome, Groveland Tap or the Bulldog. If I must go to Minneapolis, Town Hall is fantastic! I'm a home brewer and love some of the beers they put out!
What about craft beer stores? Where are the best selections, and who has the mixed six packs? I've heard Pairings in Minnetonka is pretty good.
My impression of Pairings is that they're long on style and price, not enough good beer choices. Try the Four Firkins in Minnetonka for great beers, if you're south of the river head to Blue Max in Burnsville.
Muddy Pig (belgian)
Happy Gnome (american craftbrew)
Bulldog (any location)
Stub & Herb's
To buy craft beer:
Heritage Liquor (for craftbeer and imports it's a hidden gem out in Maplewood)
Four Firkins (you'll overpay, but it's a cool little shop)
Chicago-Lake (always has something I want and the prices are low)
The Bulldog has a good selection, espeically if you are into belgian beers. As far as buying, I have found South Lyndale Liquors (53rd and Lyndale) to have a good selection of both 6 packs and bombers.