Amtrak has the Hiawatha service that runs between downtown Chicago and Milwaukee, with a stop at MKE airport.

If your trip is early enough in July, you might want to consider checking out Milwaukee's Summerfest. It's advertised as "The World's Largest Music Festival" and runs from June 29 - July 9. It's a great party and is an easy walk from Amtrak's Milwaukee downtown station to the lakefront festival grounds.