Drive around and meet people.
Ask those who live there.
Interview the school professionals, coaches, etc.
Park in a neighborhood and see who notices you sitting there in your car.
Walk and talk.
Of course choosing a local real estate pro can help you save a lot of time.
(Not me, I'm on the Cape, but I can help you choose a local pro when you are ready.)
(Please note: when you choose an answer as a Best Answer, or at least give a thumbs up, it helps those who answer questions here.)
Generally speaking, the Schools in the Chestnut Hill sections of Brookline and Newton are highly regarded. Since MCAD (Massachusetts Commission Against Descrimination representatives have forbidden Realtors from commenting on schools so as not to steer buyers, you may want to check out on eof the following web sites...http://profiles.doe.mass.edu/, http://www.greatschools.org/, http://www.bostonmagazine.com/articles/2012/08/boston-best-s or http://www.neighborhoodscout.com/ma/schools/.
Best of luck with your research.