The subway or the "T" is definitely the way to go. I suggest staying close to downtown Boston, because there is a lot to do and see right there without traveling. Your kid would probably love the Childrens Museum if you think "real" museums would be a yawner. It's big with lots of interactive, hands on stuff to do. Things like, a scale that shows you how much you weigh on the moon, optical illusion gizmos, etc. I had to drag my kids away from this one display where you line up your faces in a "mirror" and see what 2 of you look like merged.. lol Anyway, there's tons of great restaurants, the aquarium, Fanual Hall (a dose of history plus tons of cool shops, not real expensive, lots of food stands too)
Downtown hotels might be spendy, but even if you stay outside "Boston proper" you are not far from the action with the T. I think you can see maps/routes at
www.mbta.com (or org?) Good luck, hope you have a blast!