A fun thing to do is to go into Boston for the Boston Duck Tours.  It's an amphibian boat that has wheels to drive through the streets of Boston,then drives right into the Charles River to continue the tour. People stand on the sidewalks cheering and those on the tour have plastic duck "quackers" to quack back.  All ages enjoy these tours.

Nars, below answered most of my favourite sights. I have 3 sons and we havé visited Boston every summer for years. I highly recommend 

no. 1,3,6,8 AND the Boston Children's Museum ( regardless of ages, my kids fondest memories are from this museum). They also have the best gift shop. No. 6 is a must but you need to buy tickets ahead of time And they sell out. Boston is a fabulous city for kids and their parents.

New England Aquarium is great and on the water so a great place to walk around. Outdoor carasol nearby. Harbor boat rides right at Aquarium as is the trolley cars. Faneuil Hall is close and you could get food and souvenirs. A little touristy though. I wouldn't go here to eat dinner. Would go to North End for an authentic Italian dinner.  

Or, in another part of town, but still on the water is a restaurant called Temazcal Tequila Cantina. Great outdoor tables on water and you could go to the ICA nearby. Hope that helps.

First of all, you will not need a car. Boston  is a walking city. If it is not close enough for walking just ride the MBTA (Subway)  It is a good beginning for the kids as they will love it.  In Boston:  visit Faneuil Hall Marketplace ,  (Patrick Henry gave the "Give me Liberty or give me Death" speech here) and enjoy the shops and food.  If it is Friday the Haymarket Square  produce market will be open nearby.  When you get hungry go up to the North End  and eat fine Italian food.  Afterwards you can visit the New England Aquarium which is a short walk away.  There is also a small Chinatown near Washington Ave at Beach St east of the Common. 

Go over to Cambridge (Massachusetts) (red line subway from Park Street Station or Boston South StationS)  Roam around Harvard University and visit the Peabody Museum of Archaeology and Ethnology and Harvard Museum of Natural HistoryPeabody Museum of Archaeology and Ethnology ..this is a must for kids.  

The Museum of Science  sits on a bridge across the Charles River between Boston and Cambridge.  It is Kid Heaven.  

You can walk the Freedom Trail and visit the Boston Common

If your timing is right, go to Fenway Park to see the Red Sox. 

 I just looked at the MBTA maps and you can get to Salem (Massachusetts) and Lexington (Massachusetts)by train.  The House of the Seven Gables is in Salem and the town is full of stuff related to the Salem Witch Trials. 

I hope you have a great time in Boston.  I lived there and I love the city.  

1) Swan Boat ride at the Boston Common

2) Imax show and the planetarium at the Museum of Science

3) Faneuil Hall Marketplace (dozens of food stalls)

4) Educational 2.5 mile hike of the Freedom Trail

5) Tour the Fenway Park

6) Boston Duck Tours for fun Boston insights, great views of Boston and the lovely Charles river

7) Whale watching at Boston Harbor Cruises

8) New England Aquarium

9) Massachusetts Institute of Technology and Harvard University campuses

10) Copley Square

11) Harvard Square

Tons of food options everywhere. If you enjoy Italian food, don't miss the North End (Boston's little Italy).

Enjoy!

Boston is a very friendly city for kids 

I would also recommend the Boston Tea Party Ships & Museum, tour of Fenway Park and walking around Harvard Square. The aquarium offers great whale watching boat tours. Be sure to rent bikes to move around the city. It's a great way to get out to the Museum of Fine Arts. For meals, be sure to go to the North End for dessert. My kids like Gaslight, Met Bar & Grill and the Legal Sea Foods out on the waterfront. Which is a fun area to explore in the evening. Enjoy!!