The Electric Fetus is quite nice. Crazy selection of cut-outs that are mostly OOP.
I would recommend the Minneapolis Institute of Art over the Walker all day long. While not as on the cutting edge as the Walker, you are going to get a much more rich experience at the MIA. Their permanent Asian art galleries are on par with the Smithsonian's collections.
St.Paul's Como Conservatory recommendation will get another vote from me. I go every year. They have recently expanded.
For dining, I would recommend the 112 Eatery in the Warehouse District in Minneapolis. http://www.112eatery.com/ It has made the top of everyone's list as the best thing, and at a reasonable price!
For lunch you can stuff yourself for about $7 at the New Delhi lunch buffet. Top notch Indian food set up buffet style. http://www.newdelhimn.com/
If you dig sushi, Nami is the place to go. Great space, great food. http://www.namisushi.com/
By that time the Minneapolis Farmer's Market will be in session; it is good people watching and they have vendors with prepared foods ready-to-eat. Plus, you can buy that special someone some flowers there. http://www.mplsfarmersmarket.com/
I can recommend more things, food, entertainment, whatever. I will leave you with a hidden gem right in downtown Minneapolis -- Khazana. http://www.khazana.com/ This little shop specializes in antique Indian jewelry, tapestries, folk art, paintings, instruments etc. If you ask the nice gentleman that works there, he will take you into the basement -- it is the warehouse for their striking online Indian music store. You can browse while he makes recommendations. It is a small place, but quite unexpected. The lady that does the jewelry will tell you all of the stories behind the pieces, as she travels to the Subcontinent each year to buy all sorts of things.
There is plenty to keep ya busy!