within walking distance of the State capitol building--the best bar is 'Come Back Inn'. Only a block away, the Cardinal Bar might appeal to you. The Great Dane up the street is popular too, a micro brew pub--try the Pepper beer if they still have it.
Check out the Memorial Union on campus also...600 Langdon St. You'll need a Student ID to buy beer, but you can get a free day pass for that right there--just say you're from out of town. Music on fridays and saturdays outside. Best hangout in Madison.