That would be your best bet. I would drop off the luggage at the hotel I would later check-in, instead of trying any hotel. Besides, how can you be sure you will get your bag back if you just simply hand your bags to any bellman at any hotel?
Otherwise, Marshall Field Dept Store (founded in Chicago) downtown has storage service (free) at the top floor.
Otherwise, Marshall Field Dept Store (founded in Chicago) downtown has storage service (free) at the top floor.