Take the $$ and run. WashU is king in St Louis and Chicago. And cheap cost of living to boot.
I think all 3 schools are so good that choosing one or the other won't make a ton of difference.
This is wrong. As GULC already indicated, WUSTL is definitely not king in Chicago. It's respected, but not king. I'd toss it in with all the other solid schools vying for spots in Chicago, but below UIUC (UIUC just has some powerful placement ability in Chicago due to alumni). From OCI, my estimation of Chicago placement is: Chicago > NW/Michigan >> Illinois > Other solid midwestern schools (Minn, ND, Wisconsin, Indiana-Bloomington, WUSTL, etc.) > Kent/Loyola/Depaul >>> NIU/JMLS.
I wouldn't even go far as to call it king in STL. Its rep goes far and it's a good school, but there are a number of firms that look suspiciously at WUSTL. STL is a secondary market where ties are not required, but they are often important. Kids at WUSTL do great if they are in the top 1/3 or so or have ties, but anywhere outside that without ties and things can get dicey. Not impossible, just tough.
I'd say Michigan in a heart-beat, especially if you are looking at Chicago and want the best options. If you want to go with money, I'd go UIUC for Chicago (unless you just fall/fell in love with WUSTL) -- I think you'll be eligible for in-state after your first year and the alumni network in Chicago for UIUC kids is pretty strong.