Actually it doesn''t even have to be your hotel. Most decent

hotels bellmen would be happy to collect extra tips for putting awy your bags. They generally don't ask if you are a hotel guest (you can act like you just checked out).

Chicago airport hotels (especially the ones at the terminal) do not store bags for non-guests after 9/11. On one of my trips I really have to push the envelope with the Ohara airport Hilton to get them to store my bags while I visited the Art Institute.