Quoted from Grangeomatic:CP Pinball, on the IL side of STL, is very much worth a visit, but they may only be open on Saturdays.
https://cppinball.com/
Yes, open to the public on Saturdays only. Very close to it is the Pump House Bar and Grill in Wood River, they have a pretty good selection of pinballs, maybe 16-20 games (owner is a pinsider The_Pump_House ). Also have the St. Louis Escape just south of downtown with a pin room, and the City Museum has an EM collection (https://www.citymuseum.org/). There are some other places in an around St. Louis as well, these are the ones I am familiar with.