The Paul Revere Park in Charlestown works double duty (no pun intented) for babies and doggies. The playground is small and fenced-in with a massive covered slide, and the dog park is huge, without a fence, with plenty of green heaven for doggie to doggie contact. There is a little something for all your "children."
It's not the easiest place to get to, but there are a few parking spots tucked away, and a nice walk from the pier behind the Residence Inn that takes you under the Washington Street Bridge. If you're walking back and forth from Old Ironsides to the North End along the Washington Street Bridge, you can't miss it. It's such a picturesque spot that we saw "This Old House" filming with the Zakim Bridge in the background.
Lots of helpful information on the Harborwalk website.