I agree that New England, Washington DC, and Western NY (Niagra Falls) are three different vacations. By the same token, you can accomplish the equivalent of two vacations in 12 days. But not three vacations.
While you can walk around Boston in a day, that's all you'll be able to do in that day, i.e., walk around Boston. In essence, you can visit the Freedom Trail in a day, enjoying stops along the way such as Faneuil Hall, and perhaps do a duck tour... maybe. But you'll need a lot more time to "visit Boston". If you tried to do it all in a day, you won't be able to fit in a game at Fenway (which might be a very attractive part of a vacation in Boston for some), and you surely won't be able to visit Salem (3/4 day, between the maritime museum and all the Witch trial historical stuff, not to mention the Peabody-Essex Museum if your son is inclined toward historical art and culture in any way).
You can spend most of a full day in either Old Sturbridge Village or Plymouth Plantation (though I would recommending doing both in the same trip, since they "cover the same bases"). You may also want to consider fitting in a whale watching tour while you're here.
Then there's Minuteman National Historical Park, which actually meanders in sections from the Lexington Common ("the shot heard 'round the world"), through the Old Battle Road that winds through Lincoln MA ("The redcoats are Coming!"), complete with restored colonial homes with scheduled and self-guided tours, to Concord and the Old North Bridge. And despite living here for so many years, I only just realized that beyond the Old North Bridge is The Old Manse! (Ralph Waldo Emerson and Nathaniel Hawthorne both called the Manse home for a time.)
And then there's Maine. There are lots of options for spending a day in Maine, though I don't really associate Maine with someplace I'd take a 13 year old to, necessarily. I think there's more than enough to full a full week just within Eastern Massachusetts itself.
And if you think it is difficult to fit "Visiting Boston" into just one week (and after reading what I wrote above, if I did a good job, then you should think it would be difficult to do so), "Visiting Washington DC" in just one week would be even more difficult. The Capitol; the White House; the Washington Memorial; the Jefferson Memorial; the Viet Nam War Memorial; the Roosevelt Memorial; the King Memorial; Arlington National; the Smithsonian itself, and its associated museums - History and Technology (name has changed, but I don't remember what they're calling it now); Air and Space; Frick (art). Then: The National Archives; the Bureau of Engraving and Printing; the Holocaust Museum; Ford's Theater; Kennedy Center. And that's just right off the very top of my head. As I sit typing this sentence a dozen others just popped into my head. And I've never lived there ... that just from my own personal visits to the place, over the years. I'd type some more in, but I've got to get ready for church.
