I live in Maine and I just wanted to say that if you can, check your library for a book called Fun things to do with Children New England. It is on
Amazon too but your library might be able to get it for you for free. I actually own it because I got it in our library once and loved the ideas in it. There is over 100 suggestions and you can easily see what is free and what interests you. It has some great suggestions and often I will pick it off the shelf and look though to find a fun day trip at the last minute on a weekend. There is so much to do in New England.
Also, if you have a Children's or Science museum membership where you live check and see if you bought reciprocal membership. Most places offer it. We have a membership at the Portland Children's museum and Boston Science museum. With those purchases we have been able to go to the children's museums in Boston, Augusta, and Portland OR. Plus we have been to multiple Science museums on trips for free because of the reciprocal membership. It might be something to look into if you do have one and want to let the kids run around for a couple of hours one day. The Boston Science museum is really cool if you do have one. You can easily spend several hours there.
Strawberry Banke in Portsmouth is also really neat. My kids love it more then Sturbridge because it is smaller and less crowded. It is also really affordable. You can walk around Portsmouth for free and it is a super cute, fun town. Both places are amazing though. And if you make it up further North there is tons to do in Conway NH, and Portland ME. For example, you can catch a ferry ride to the islands and spend the day riding bikes and hiking or spend time walking in the Old Port and going to the museums. Lots of light houses offer tours too. Depending on the season, Conway has skiing, hiking, water parks, and mini golf. Not sure if that would interest your kids but my kids love stuff like that.
I agree with others on the historic can't miss stuff. Such as Plymouth Plantation, and the Mayflower (both not cheap though!). Freedom trail, and Fanuiel Hall. There is a free Firefighter museum in Boston too. But it isn't always open. Swan boats are fun too! Have a great trip!