C.W.
Mill City Museum for a look at how Minneapolis began: http://www.millcitymuseum.org/
Also, be sure to check out Mill Ruins Park and the Stone Arch Bridge while you're there: http://www.minneapolisparks.org/default.asp?PageID=4&...
Have breakfast at Hell's Kitchen in downtown Mpls. (I strongly recommend the lemon ricotta pancakes): http://www.hellskitcheninc.com/
The Minneapolis Sculpture Garden/Walker Art Center: http://garden.walkerart.org/index.wac
Minnehaha Falls. So much to see you can spend a whole day there. (I don't know where your hotel is, but you can take the Light Rail to get there--kinda fun): http://www.minneapolisparks.org/default.asp?PageID=4&...
Minnesota Centennial Showboat in Saint Paul is lots of fun. This year they're presenting The Vampire. It's old-timey theatre (melodrama - you are encouraged to cheer the heroes and boo the villains) but done really well. The show this year is really good and the actors are great singers: https://theatre.umn.edu/showboat/
Unless you're big into shopping or amusement parks, I'd avoid the Mall of America. It really is just a big mall with an amusement park.
I'd suggest some things on the University of Minnesota campus, but it's really torn up right now with Light Rail construction. Avoid the U, too.