I have boys 10 and 12.
Their favorite activity on the Freedom Trail is climbing the Bunker Hill Monument, touring the USS Constitution and USS Constitution Museum.
They also enjoy the New England Aquarium, visiting George's Island, walking around Rose Kennedy Greenway. On Thursday evenings the ICA is free, we do a quick walk thru (sometimes the exhibits are more adult theme) but the harbor view from the ICA is worth the free visit! We continue walking the Boston Harbor Walk towards the North End via Fan Pier.
They also enjoy the Boston Common and the Boston Public Garden. I think your kids would enjoy a Boston Duck Tour, too.
We are Science Museum members, if you are members of your local museums, you can get reciprocal free visits to The Museum of Science. We are still members of the Children's Museum, too. There are still exhibits at our Children's Museum to entertain my kids at the Boston Children's Museum even though they are getting older. It might be worth a visit on Friday night after 5 PM for their $1 admission night.
We also enjoy going to Red Sox games.
I took my 12 year to Chicago in April and we LOVED your city! We attended Wrigely Field's 100th Anniversary game and got to experience being a Cubs fan for a day! (Cubs with a strong lead, two outs, Cubs needed one last strike to win the game in the 9th inning.....yet, they lost the game! )
BTW - in Plymouth, my kids really enjoyed their Lantern Ghost Tour. They enjoyed the Harvard Square Ghost Walking tour, too, in Cambridge. I know they have ghost tours in Boston, too, but we have not participated in those tours.