Wrigley Field Chicago has a First Aid area that has a couch & curtain for privacy, which nursing mothers can use as a space to express breastmilk for their little ones.
Their website stated that: "The First Aid office is located on the first base side of the main concourse. Please ask an Ambassador for directions to the nearest restroom."
Note: Moms you are also legally allowed in the state of Illinois to openly breastfeed your baby in your seat if you are comfortable doing that, regardless of what onlookers say.
Though Wrigley does not have a dedicated nursing mothers lounge yet, we've contacted them to make efforts to build one like other major league baseball teams have done including Safeco Field in Seattle and Great American Ball Park in Cincinatti.