I don't exactly jump at the chance to go to baseball games, but the place where White Sox play is uniquely awful. Wrigley field has a Red Line stop directly next to it and it's a very old place full of character. The Sox place is like bench seating at a McDonald's. I wind up at a baseball game every couple years. Usually the best time is just watching somebody who spent $200 on beer try to navigate a lot of stairs.
I have seen the Chicago Sky WNBA team play a few times. The tickets are cheap, their court is easy to get to (it's right next to the downtown convention center) and the players and audiences are decidedly queer, which is a very different vibe from other pro sports events. It's also a lot easier to interact with the players. The whole WNBA thing came to my attention because there's a team called the Valkyries, which is the name my partner used to work under. I bought a team shirt with "her" name on it and eventually we decided we had to actually go to a game. My partner is ironically more interested in football, but I've taken several out of town guests to see either Cubs or Sky mostly because both of their stadiums are extremely close to train stops. The football stadium is also accessible but 1. Apparently they're not playing there much longer and 2. I'm not OK paying $300/person to sit through a game I don't care about in the open air, right off the lake shore and in the fall.