Twins games are the hot cool thing right now, saw lots of people downtown today after the game. Lots of them taking the bus and the LRT .. awesome!
Stroll around downtown, take the bus up and down Nicollet Mall - free now from 3rd (by the library) to 12th (by convention center).
Admire our unique skyways crossing overhead, making it possible to walk most of downtown without every setting foot outside in the frigid winter temps!

Take a pic with the Mary Tyler Moore statue in front of Dayton's.. err Macy's. (It will always be Dayton's to this MN gal!)
Not sure when it closes but Macy's 8th floor auditorium has the flower show going on right now. Take the escalators all the way up, it's fun to see the marvel of this very old department store location. There are nice restaurants on the top floor or the deli on basement level.
The farmer's market along Nicollet Mall should be opening soon, or go to the Minneapolis one on the weekend.. it's wonderful and BIG!
Haven't gone but hear good things about Mill City Museum, good for the history lovers. They also have a farmer's marke ton weekends but they have a later kick off date. Most of it is organic, sustainable/local agriculture and some food trucks that get rave reviews. (Twin City people are weirded out by street food, it's a rare thing to have any food trucks).
If you feel adventurous.. go to Lake Street Global Market, lots of yummy places to eat and unique shopping.
From downtown, take the LRT to Mall of America. Good chance to see a few neighborhoods along the way. Passes by Minnehaha Falls area, very pretty and very old... Runs under the airport, runs next to Fort Snelling and the cemetery too.
other ideas...
Minneapolis Institute of Arts is free
Sculpture Garden is free and a chance to see the famous Cherry Spoon.
Northeast is a fun spot for bar hopping, food and shopping.
Science Museum is worth the money and the trip into St Paul.
MN History center is a pleasant visit too.. no longer free.. BOO!
There are tours of the capitol building if you like architecture.
There are tours on Segways in Minneapolis for the old mill traces and the stone arch bridge. Never done that.. but I see them a lot and looks like fun.