I also would like to suggest to rent a car for a long-term period from a major agency. You should go off-airport to a local location. I.e. in case you rent a car at Avis at Chicago-O'Hare you have to pay almost 25% in taxes only. If you are willing to take a ten minute cab ride to i.e. Park Ridge not far away, then you have reduced taxes of roughly 7% only.
