Unfortunately there is not one right by the MOA. But it's not terribly far away. Mystic Lake, SW of the airport, is about a 30 min drive, maybe a little less, I've never done the route from the airport. All casinos are run by Native American reservations, with the one exception of Canterbury Park horse track which has a card club and is about 20 min SW of MSP. (It simulcasts during the winter.)

There are plenty of good theater shows to see as well, if you haven't heard. The Star Tribune has a good listing of shows here. (go to the box in the upper right that is titled "Entertainment Finder" and make sure the "OnStage" tab is selected. But it also allows you to search the music and art showings as well, however, by clicking the corresponding tabs.) The biggest theaters are the Guthrie, Ordway, Orpheum, and Historic State theaters. It often isn't cheap, though.