S.G.
Oh, it'd be fun to go see a play! They are performing Ramona Quimby at the Children's Theater right now. Maybe you could do a special outing to get your hair done and dress up for the show. You could go to a matinee and then to a nice restaurant afterwards.
Otherwise, I also thought about a road trip to one of the Laura Ingalls sites if you'd like to get out of town. Here's the website for the Walnut Grove location: http://www.walnutgrove.org/.
Historic Fort Snelling is also cool. And the Science Museum and the Mill City Museum are both fun.
I think it'd be fun to go to the Mill City, Minneapolis or St. Paul farmer's market on Saturday morning, too (the Mill City Farmer's market is right by the Mill City Museum). And, if your daughter like flowers, you could do a trip to the Minnesota Landscape Arboretum http://www.arboretum.umn.edu/.
Have a great time!