Skip the Mall of America friend. Its a mall. Do you have a Gap where you live? Just go to there.
As a Minneapolitan, I would say, come in the summer. Rent a Nice Ride bike (niceridemnorg), Bike around the Grand Rounds Scenic Byway, check out the Midtown greenway, chain of lakes, downtown, midtown and uptown. Get some beer at Town Hall, some pizza at Pizza Luce, and some fish at Sea Salt. See the creek and the falls, talk to people. Drink some Surly.
If you spend a long weekend just being outside in Minneapolis in the summer, you'll never want to leave.
I just moved to the Twin Cities from Tennessee a few months ago and love it here. You'd of course want to come in the summer. The parks and lakes in the Twin Cities are unparalleled. The food and drink (particularly in the Uptown area) is great. There's really nothing like it.
If you end up heading south I highly recommend Chattanooga, TN (and pay a visit to The Terminal Brewhouse for the Magnum PA).
The beautiful country around New Ulm [...] is a great reason
I spent 20 years in New Ulm and it is certainly an awesome place to stop. We have the 3rd tallest copper statue in the United States. German food and heritage EVERYWHERE(remember that statue?). Good food, great drinks. Flandrau state park - Hiking, swimming, camping, river access!
You can check out Putting Green, Inc. for some miniature golf. There is river access all around. Snowmobile access during the winter, indoor and outdoor ice skating, plenty of hotels.... Used bookstores, a charming downtown, gift stores...
Despite all of the comments about how much better the summer is than the winter, I really do appreciate the variations in seasons. Favorite winter things to do? Holidazzle, cross country skiing, St. Paul Winter Carnival, Centennial Lakes ice skating, and getting warm and comfortable at a great restaurant.