The Boston Museum of Fine Arts has a nursing room across from the restrooms on the first floor near the half-circular hallway that connects the mid 20th century gallery to the American galleries. It's off the Hemicycle gallery, and there's also baby changing rooms throughout the museum.

Mom Brooke R. wrote in October 2012:
"they are stroller friendly, kid friendly, and the bathrooms were clean & had changing stations.  There are also a number of family bathrooms and a private nursing room."