FYI, anything that is state run (Minnesota Science Museum, state parks, etc) probably won't be up and running by the weekend due to the State Government shut down over the dispute of our state budget. However, city parks and museums will be functioning. You should check out the "Chain of Urban Lakes." Rent a kayak or canoe on Lake Calhoun and canoe between the lakes. Eat lunch at the Tin Fish on Lake Calhoun afterwards. There will probably be some live music (if you haven't had enough of it by then) at the Lake Harriet Band Shell if that interests.
For Dinner, I'd stay around in the uptown area and hit up Chino Latino, which is really popular among the yuppies. Or you can head over to Lyn-Lake (Lyndale Ave and Lake Street) to visit Herkimer, a brew pub, or The Lyndale Tap House. If you're feeling adventurous head to Moto I right next to Herkimer and visit the only sake brewery in the United States and eat some sushi!
That's all I got. again, make sure your adventures don't lead you toward any state-run attractions.
Oh, and the MOA isn't all it's led out to be . . .