The Twin Cities are home to a great variety of museums, from the Childrens' Museum to the new Science Museum to the Weisman Art Museum, there's bound to be a museum that suits your interests. Here are a few possibilites.
Vineland Place, Minneapolis, Minnesota
The Walker is a museum for contemporary art--which means you're as likely to see a dress made of steak as anything else. But don't let this dissuade you--if the weather is at all cooperative, go to the Sculpture Garden, an outdoor collection of modern sculpture, including Cherry and Spoonbridge, which is possibly the most recognizable piece of art in the Twin Cities--trust me, 40% of all pictures of Minneapolis feature this gigantic sculpture of a spoon and a cherry. The Sculpture Garden even inspired a song by rock group Semisonic. All in all, the Sculpture Garden is worth the trip over to Minneapolis by itself--and while you're there, you can stop in and see a play at the Guthrie Theater, which is attatched.
333 East River Road, Minneapolis, Minnesota
Located by Coffman Union at the University of Minnesota, this garish building is world famous--or more appropriately, world notorious. No less a luminary as Prince Charles decried its Frank Gehry-designed metal ediface as classless and ugly. Decide for yourself whether the shiny Weisman, home to a varying collection of modern art, is beautiful or, as one U Student put it, "like a crumpled wad of tin foil."
http://www.artsmia.org/index.cfm
2400 Third Avenue South, Minneapolis, Minnesota
The most staid of Minnesota's art museums, the Minneapolis Institute of Arts boasts a wide variety of classical art from across the world, and the past 4000 years. You could spend weeks traveling the halls of the MIA--and no meat dresses here!
http://www.smm.org
120 West Kellogg Boulevard, Saint Paul, Minnesota
The new Science Museum of Minnesota is a phenomenal way to see the world of science. The building, completed in 1999, boasts 8.5 acres of floor space, and almost two million different items. From dinosaurs to deep space to the Mississippi River that the Science Museum overlooks, all things scientific are covered here--and it's located right in the middle of Saint Paul, a short walk from the Radisson City Center.
http://www.mcm.org/
10 West Seventh Street, Saint Paul, Minnesota
Located in the heart of downtown Saint Paul, the Minnesota Children's Museum offers a range of activities for children six months to ten years old. The activities are hands-on, so kids can have fun while still learning something. And it's handy to the reception site, and just a short walk from the Radisson City Center.