A friend of mine recently listened to me describe my DS (a quirky gifted 4th grader) and immediately suggested we look into the school she used to teach at -- Fayerweather in Cambridge. Its seriously pricey, but she said its amazing. She described to me what she did for the one truly gifted kiddo she had in her class once, and it sounded like a dream. And that was just the expectation there...
I'm from a tried and true public education family (both my parents, husbands parents, and my brother in law are or were public school teachers) so a private elementary school is a non starter for us (plus its too far AND too $$ for us for 5th grade...) but if you don't have those issues, it might be worth looking into. Trust me, I had a moment of trying to figure out how to make it work!!
Also, if you aren't 100% committed to living in Cambridge, in addition to the other places folks have mentioned, the McAuliff school (a public charter) in Framingham is entirely project based and might be a great fit for the right gifted kiddo since you can work within your own range in a PBL curriculum. I am not entirely sure which communities it draws from, but perhaps one that might be a decent fit for you living wise (nothing quite like Cambridge though!).
