I live about 40 miles west of Chicago and drive a little of rt. 30. I think route 30 is a mistake, it is a very rough and narrow highway with a ton of little towns to go through. If you want to be close to Chicago, take the interstates, 80W to 355N (tolls) and then take 88W (tolls again)past Aurora. I would stay on 88W and then you can choose if you want to get back on 80 (88 will take you there near Iowa), or take 39N up into Wisconsin and take 90 west through the South Dakota.
Either route seems to take forever as Iowa and Minnesota are a real drag to drive through. I personally like to go through South Dakota. Allow plenty of time to drive from one side of Yellowstone to the other, it is HUGE and you will be driving slow.
You are planning a great trip, enjoy!