Here are a few brewpubs reasonably near there:
Town Hall Brewery is nationally recognized as a place to visit if you're in town, they have some cask ales on beer engine as well as some very fine house beers on tap.
I have not been to Rock Bottom in quite awhile, my buddy was a floor manager there 10-15 years ago. Todd Haug, the brewer at Surly Brewery, was the head brewer there for I think ten years or so before he threw his lot in with Omar over at Surly. It's in the City Center, downtown, you can park under the mall and get your parking ticket validated so it's free parking downtown--what a deal! (also bring your cue, they have pool tables)
And for some authentic Minneapolis ambience you should hit up the Herkimer brewpub, over on Lyndale. Haven't been over there in awhile, either. The beer is pretty good, the food can be so-so.
Also, while you are there, assuming you have somewhat of an open mind, you can walk about 50 feet down the block and visit "the first sake brewery restaurant outside of Japan."
Highly recommend moto-i if you appreciate good sake. If you don't, then I recommend you start.