At the end of the last US trip for work I had three days in New York, mostly seing things at night and one short morning to walk around.
The bad thing about business trips is that you mostly only see cities at night. During day you have to work, at night you have some time to stroll around.
Chicago is the place where the skyscraper was born. Together with New York modern architecture started in Chicago at the end of the 19th century.
The Field Museum of Natural History is one of the largest museums in the world. It features everything rich people could get away with stealing and killing in the late 1800s: egyptian mummies, dinosaurs, native americans and any form of dead animals.