The closest air pump reference I could find online is on a third-party site at https://www.bike2campus.com/university-of-chicago-uofc.html which suggests there is at least one:
Air Pump(s) on Campus:
By Bartlett Dining Commons, just South of the West entrance.
Does anyone know of any more?
I also found a semi-official reference to the same location in the Google cache of a now-taken-down webpage:
Every dorm has a bike storage room for the winter months or rainy days and bike racks outside. Bartlett Dining Commons has a little station where you can pump your wheels or tune up your bike.
But I have no idea whether that station is accessible to non-undergrads. Will update if I get a chance to go and look.