Hi J.,
I used to live in Belmont before I had kids, but I know there aren't many options in town. However, if you're willing to drive 20 minutes, Bedford has a brand new fenced-in town playground as well as an awesome indoor playroom open to the public. It's run by the Bedford Family Connection ($20 annual membership is open to residents of Bedford & surrounding communities, must have at least 1 child age 5 or under) and is open during the school year. The playroom is located in the basement of First Parish Church at 75 Great Road (large church w/green in center of town) and is open weekdays from 9:30-11:30AM. A snack is provided at 10:30 as no outside food/drink is allowed (except for infants on bottles). One half of the room is all toys/books/games with a play kitchen, changing table, mini slide... and the other half has a child-size lunch table & chairs in the midst of a large open play space. This is where moms with infants sometimes sit for tummy time.
There is a daily charge for visiting the playroom: 50 cents per child for members or $2.00 per child for non-members. Since the annual fee to join is only $20 (and all activities are free unless otherwise stated in the monthly e-newsletter or weekly email reminders) it is really worth it to join if you like the playroom.
For more information about the BFC and the playroom (I'm the volunteer coordinator) check out www.kidsplaybedford.com. We also organize playgroups, so you can also contact me offline and I can send you the form if you're intersted in coming to Bedford for play time. My own boys are 3.2 yrs and 20 months, so we do lots of BFC activities.
Good luck! ~N.