Things that haven't got mentioned:
ICA (Institute of Contemporary Art; www.icaboston.org) is my favorite museum in Boston. Thursday night is free and recommended for families. (serious visitors wouldn't go for free hours so your 12 yo wont bother others).
Helmond restaurant. Excellent food from Afghanistan and the price is pretty reasonable for restaurant of that class. None of my out of town guest gets disappointed. Reservation strongly recommended.
Some of the museums at Harvard University are pretty good. MIT Museum is interesting but in a more techie way.
A walk across Longfellow bridge between Charles/MGH and Kendall/MIT. This 100-year-old bridge (classified as "structurally deficient") is planned to be replaced by a new bridge in a few years, and it may not be there when you return to Boston next time.
When you do freedom trail or go to the area nearby, notice Zakim bridge (Bunker Hill bridge). It's probably the most controversial bridge design (esthetically) in Boston.
Things that already got mentioned:
North End. If you see Boston's North End, you'll know that NYC's Little Italy is nonexistent.
I don't know if Harvard Square is that interesting. Certainly, people there are not strange enough. (If you want to see really strange people, go to Diesel cafe in Davis Square... Oh Charlie's Kitchen in Harvard is probably strange enough, too.) But the Harvard museums are in there, and there is also Club Passim, etc...
There are lots of places to watch good play but I guess that wouldn't be good with 12 yo.