Liz Weddle's recommendations are the Mia or the Walker Art Center. The Mia is free admission with art from a variety of time periods and cultures. The Walker is contemporary art, and admission is $18, but it also has a free sculpture garden which is where you can see the classic "Spoonbridge and Cherry" sculpture.
Becky Halberg's favorite local attraction to visit with her family is Como Park Zoo & Conservatory. There is a little bit of something for everyone—lions, tigers, and bears (oh my!)—as well as greenhouse tropics and beautiful gardens to walk through. The best part—it's free admission.