Chicago is fun. Don't listen to them.
It is easier to drive. But if you really felt more comfortable on train then you could do that too.

I'm a little late to the party, but...
There is a regularly scheduled "Coach USA" bus (similar to Greyhound) that travels between Chicago's OHare Airport and Milwaukee's Gen Mitchell International. I think it runs hourly.
A one person, one-way from OHare's Terminal 5 (international) to Mitchell is about $30. The bus also goes to the Milwaukee Intermodal Station (Bus/Train). This is a couple blocks north of the HD Museum.
https://www.coachusaairportexpress.c...e/TimeSchedule

There are taxicabs and Uber/Lyft shared ride drivers available within a few feet of where the Coach USA stops at the Mitchell main terminal. My advise, use Uber or Lyft. At the Intermodal, you'll have to use a smart phone app anyway.

There are a few nice hotels/motels within a few blocks of the airport. Hilton Garden, Clarion, Hyatt Place, Best Western Plus. There are a couple of very nice hotels within a few blocks of the HD Museum. DoubleTree and Hilton Milwaukee Center is north, Iron Horse is south

If you have any questions, shoot me a PM. I live in the area