Since the Boston winter is so long, here are some ideas for indoor play spaces for your little ones.
Museums: Both the Science and Children's museums have areas for little ones to play. And the Science Museum is also fun to walk around and see different interesting things. Annual memberships usually make sense if you are going to go more than a couple of times per year.
Aquarium: Very fun to explore and annual membership also makes sense if you are going to go often.
Here is a list of some indoor play spaces I have heard about. Some have certain days of the week and times for open play. They all charge a fee
Imagine in Cambridge http://www.imaginecambridge.com/
Soule Recreation Center in Brookline (not sure how clean it is, but worth checking) http://www.boston.com/yourtown/news/brookline/2014/04/brooklines_winter_indoor_play_program_safe_and_free.html
Kids-street in Needham: https://www.kids-street.com/ I don't know much about it but it looks like it has some open play hours for toddlers for a fee.
Exxcel Gymanstics in Newton: http://exxcel.net/climbing/open-climb.php It has limited hours but one Mom from class said it was lots of fun!
Cobblestones in Waltham: http://www.cobblestones4families.com $10 per visit or $80 for 10 visits. They have Open Play hours. Space is clean and well-maintained but not very big. Better to go early.
Kids Fun Stop in West Roxbury: http://www.kidsfunstop.com/
Inside Playground in Watertown: http://www.bostonindoorplayground.com/ Some of you like it, but some find it not as clean and a bit busy.
Jam Time in Natick: http://www.jamtime.com/
Mama&me in J: http://www.mymamaandme.com/playspace/. They have play hours 3:30-5pm m-f. Space with lots of toys(kitchen, puppets, gym area with balls, books). The main difficulty is parking. Sometimes you have to circle for a space to open up. It's at the brewery building in JP. $10 per visit or $80 for 10 visits.
As for free places to go with your child in the area:
Magic Beans, Brookline: It has a small play area in the center of the store
Henry Bears Park, Brookline: They have some toys out children are allowed to play with
Natick Mall has a children's area but I hear mixed reviews about it (some caregivers say is a bit dirty and can be crowded).