Our science museum rocks
http://www.smm.org/ You don't have to see the King Tut exhibit there right now (that is pretty pricey, although interesting). There is a lot of other stuff to see and do if you just get general admission tickets. The Omnitheater is also good, of course -- would recommend booking those tickets a day or two ahead of time to make sure you get the times you want if you choose to do that.
Although the museum is over in St. Paul, it is pretty easy to get to from Eden Prarie (which is south of Minneapolis, and the museum is on the south side of St. Paul).
We also really like the Minneapolis Institute of Arts.
http://www.artsmia.org/Science museum and MIA are 2 of our favorite destinations too! Mill city museum downtown Minneapolis and MN history center downtown St. Paul are fun too. If you want something outdoors, the sculpture garden near the Walker art museum (which is great) is a great way to spend a couple hours. Como Zoo and conservatory is free (donations only), you can be outdoors at least part of the time, and right in the city.
I was also going to say, there are MANY events going on that weekend in town. Our neighborhood in St. Paul is having an art fair on the 4th of June, Flint Hill Children's festival is going on in St. Paul (we love this! Happens to be walking distance from the Science museum so you could hit both.)
http://www.ordway.org/festival/Grand Old Day on Grand Ave in St. Paul
http://www.grandave.com/grandoldday/Probably more stuff too!
It's a great time of year to come here! Hope the weather's good for you.
