Drano! Luckily, I am 1 of 3 people on this forum who actually live in the city. Im so happy to actually recommend places inside the city limits as most people just play out in the burbs.
There aren't many places with ALOT of pins. Most locations only have 1 or 2. But there are a couple places I really like that have a few games.
Logan Hardware: Its a record store on the north side. They have maybe 7 pins set up at a time in their big free play acrade in the back. All you have to do it buy something up front and you can play as long as you want.
Bottom Lounge: Music venue and bar on the near west side. They have 6 pins upstairs, all 90's era, and they have good beer too (if you are into that). This place is also a couple blocks from my office. We go here a bit.