We have been to the library many times especially when the kids were little. Last I knew, the library has two mornings that each has an hour or so sing-and-play with babies and toddlers. Make sure to check the website for various activities. Kids get to listen and sing some sounds, do some dance movements, and even play with simple instruments.
For older kids, they have lego club and chess club. For even older kids, they have computer related activities too. It’s a nice hub for family with kids in the middle of the city.
New Haven Kids! 