When in doubt, take your kids to a playground! Cheap, free fun. There are many a playground all over - but here are my local favorites:
Quincy: Wollaston Beach Playground on Quincy Shore Drive. I love this playground because it's completely fenced in. It's relatively clean. There's many tables and benches and great views of Boston. The only word of caution is you might want to pack a sweater and/or sweatshirt because it can be chilly - even on seemingly warm days.
Weymouth: Kids Landing behind the Tufts Library on Broad Street. Pretty good playground that includes two big play structures, a sandbox, and many swings. Bonus is that you have the children's room right there if you need to use the bathroom facilities or if you need an "inside break" if it gets too hot.
Hingham: Playground behind the Fire Station off Main St. The parking lot to this great spot is actuality the driveway to the Fire Station on Main St. The playground is behind the town hall. This well thought out playground with many structures, mini houses, swings and a sandbox is a great spot. The playground is completely fenced in. There are also playing fields and a track next to it in case you want to bring a soccer ball or other fun activity. Only con is that there is no public bathroom - they usually throw a port-a-potty up during the summer but trying to change a kid or help a kid in a port-a-potty can be pretty nasty.
Braintree: The most awesomest of playgrounds is right on Route 37. It's new and it's huge (it cost something crazy like $250K so of course it's going to be good). Completely fenced in and tons of stuff for the kids to do. I don't remember bathrooms there and because of it's awesomeness - can be rather crowded. Nice backup spot is the playground at Hollis School. Only con, once again is the lack of bathrooms.