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Sean BHI would just take the L everywhere, the Hyatt at Rosemont has a stop about 2 blocks away and from there it goes straight downtown, all for around $2 with no traffic problems and you get to ride more trains!
You can expect to pay about $40-$50 to take a cab from Rosemont to DT Chicago.
About 10 years ago I took the train from Minneapolis to Chicago...one of the best traveling experiences of my life!