First day I'd check out the Georgia O'Keefe paintings at Frank Gehrey's Weisman Art Museum at the U of M on the East bank of the Mississippi River, followed by hot fudge at Annie's Parlour on the East Campus in Dinkytown, where Bob Dylan hung out before moving to NYC.
Then I'd venture downtown, shopping in the skyways, and a photo-op at the giant stack of pancakes at the Mill City Museum. Outside you can ride Segways over the Stone Arch Bridge.
In the evening I'd catch a show at the Fine Line Music Cafe downtown or a play at the Guthrie Theatre on the river. Then I'd stay at Nicollet Island Inn, a cozy b&b on a small island on the Mississippi in the riverfront area.
The second day I'd check out the Spoonbridge & Cherry at the Mpls Sculpture Garden and the Walker Art Museum. Then I'd visit the ornate Swedish Institute which looks like a castle and has intricate woodwork and massive stained glass inside. On to Uptown, I'd dine at The Cafeteria, making sure to order their banana cream pie for desert - to die for!
I'd then tour the Chain of Lakes- they rent canoes and rollerblades nearby - if you canoe Cedar Lake you can see a Frank Lloyd Wright private residence on the shore. Lake Harriet has a beautiful bandshell with ice cream and summer concerts, plus a rose garden, Japanese garden, trolley, and the interesting Bakken Museum which features scientific hands-on exhibits for kids in an old mansion. Lake Calhoun is the largest with beaches and sailing. Lake of the Isles has the best views and is a block off the old Mary Tyler Moore show's house. All four of these lakes basically connect with walking/bicycling paths.
Third day, I'd hit Mall of America- shopping, minigolf, movies, dining, amusement park with flume and rollercoaster (technically its in Bloomington, just south of Mpls). Then I'd hop over to St Paul: check out the Landmark Center, Rice Park with its Peanuts statues, have a pizza lunch at Cossetta's, then tour the old James J Hilll mansion in F Scott Fitzgerald's old neighborhood. For some history, I'd visit St. Paul's MN History Museum with items from Hubert Humphrey, Mondale, Prince and Bob Dylan. That night I'd catch the Prairie Home Companion at the intimate and historic Fitzgerald Theatre, followed by raspberry cream cake dessert at Cafe Latte at Victoria Crossing, passing the Summit Avenue historic homes, including F. Scott Fitzgerald's birthplace. Then I'd sleep.