Welcome to Boston - there is a ton to do!
The obvious is the Freedom Trail, Fanieul Hall, and Quincy Market - but that is a lot of walking/shopping for kids in your age groups. There is a lot more.
First, look into a Go Boston or CityPass card - they bundle popular museums and attractions together for a discounted price. They have different offers, including trolley/duck tour packages - so you'll have to look at each to see which is best for your family. One offer includes the ferry to Provincetown and whale watching - a great day trip.
Also, there are lots of bargains - for example, the Children's Museum is $ 1.00 on Friday nights from 5 - 9 pm. The Frog Pond and play ground on the Common are free. The Museum of Science is also open late on Fridays, but can be pricey. If you are visiting family in the Boston area, they might be able to get you free tickets from their local library (many libraries have them). Libraries also might have free passes to the Aquarium.
The Museum of Contemporary Art is $1.00 on Thursday evenings. The Museum of Fine Arts is $1.00 on Wednesday afternoons (and open late).
On Friday nights, there are free movies at the Hatch Shell (along the Charles). There are also free concerts at Columbus Park (near Quincy Market) on Wednesdays, and feasts most weekends in the North End. There are daily street performers at Quincy Market too.
At the Charles, community boating offers sailing lessons very inexpensively.
If you stay outside of the city, be sure to get T passes, they are generally $15 for 7 days - well worth it!
Also, look into the Fenway Park tour and a game. The Red Sox are struggling a bit this year, so you might be able to get some tickets at a reasonable price. Right near the park is the John Hancock building, and at the top is the Ted Williams museum (as well as the Dreams of Freedom Museum).
In the summer, there are theater groups on the Common too. Check out the calendar section of
www.boston.com you'll find a slew of events and activities.
Enjoy a chowder and Boston!