I live about 30 minutes west of Boston. My recommendation for a campground near Boston would be the Boston Minuteman Campground in Littleton, MA
http://www.minutemancampground.com/
From the campground you can take the commuter rail to Boston from Ayer, MA which is about 10/15 minutes away. Or drive to the Alewife T (subway) stop off Rte 2 in Cambridge which is about 35/40 minutes away. The Alewife T stop is about 15 minutes from downtown Boston. It is on the Red-Line of the T and has stops at Harvard Square, MIT, and downtown Boston. You can find information about the commuter rail and the T at the MBTA website.
http://www.mbta.com/
The campground is also close to Concord and Lexington, MA which has a lot of revolutionary war history. I would definitely recommend the Old North Bridge in Concord.
http://www.nps.gov/mima
In Boston, I would also recommend going to the top of the Prudential building about 30 minutes before sunset. It offers a great view of Boston. Stay until after the sunset. It is nice to watch the city light up.
http://www.prudentialcenter.com/shop...tail.php?id=64