Is it a non-tour trip? I.e. you're going on your own/with friends, but not on a planned tour?
In Boston, There's a restaurant boat that sails out into the harbor and you can eat some of the best lobster on board. Just beware - you have to crack it open yourself. I was 18, freaked and had a friend of mine do it for me!
There's also Nathanial Hall, which is a very awesome place for shopping. I'm not sure where it is, but it is somewhere Boston.
You can take an hour trip to Salem, MA famous for the Witch Trials in early America. The only thing that I missed was the Witch Trial museum which has a very awesome ambiance to it....I think we were there on a Sunday and left before it opened.
Oh yes, and Cheers is a famous bar (If you have ever heard of American TV w/ Ted Danson from the 80s & 90s) its similar to that. Again, I couldn't go in because I was 18 (on with my high school peers).
Hope this helps! Sorry I haven't been to NYC or Cape Cod yet.