There is a lot to choose from. The Bayview neighborhood has a lot of the craft beer bars on or near KK Ave. Sugar Maple, Burnharts, Stone, Highbury, and Central Cafe come to mind. Brady Street is another popular bar street and can be a fun way to kill some time drinking, eating, and shopping. E. North Ave. has quite a few sport bars. BBC, Hooligans, Hotel Foster, and Von Trier all share the intersection of North & Farwell. If you want to stay closer to the stadium, Bluemound Rd and Viliet St bars run shuttles to the stadium: Rounding Third, O'Brians, Steve's on Bluemound, and Kelly's Bleachers are good. S. 2nd Street has MKE Brewing Co, hipster bars, LGBT bars, and sports bars. Commerce St. area (Near E. North Ave. bars) has Lakefront Brewery, Stubbys Gastropub, and Bel-Air. If you want more options, just ask but this list should keep you busy on google and yelp for a bit.
EDIT: Water St and Old World 3rd St. are packed with bars too.