Do you sing?

Much belatedly (after continuously residing in Cambridge since 1988) I joined the Cambridge Community Chorus two years ago. What fun it's been! We prepare and present an annual spring concert, and sing the Handel "Messiah" every December. The group is most congenial to begin with, and post-rehearsal suppers at a local restaurant make for a good way to get to know a few folks even better. Some of the more well-heeled choristers went on a concert tour of Italy last spring; in 2000, the first-ever joint performance of "Messiah" by Japanese and American choirs was Cambridge's to claim in Tokyo. We'd be "tickled" were you to join us, all the more so if you're a First Soprano. Visit cambridgechorus.org and polish your pipes!
Are you a do-gooder? Cambridge is a national capitol for that, LOL...volunteering opportunities abound. You can help out at the city's Women's Center, staff one of the homeless shelters or centers for runaway youth, work at a food pantry, put in the prescribed hours at the Harvest Co-Op grocery store if you take out a membership there, sort donated clothing for the Salvation Army, the list goes on and on and on. The weekly "Cambridge Chronicle" newspaper is chock full of ideas along these lines.
As far as getting acquainted with your neighbors is concerned, nothing works like an open house. Once you're at least somewhat settled, throw an informal cookout or cocktail party. Print flyers and place them in the mailboxes of your fellow tenants or your adjoining households. Keep it small and simple. Cantabrigians tend to be wine-and-cheese types, FYI. For hors d'oeuvres we love our Trader Joe's.
If your place has a front porch or even steps, do what I do and honor the inner-city tradition of warm-weather stoop sitting. In the space of a single evening you'll lose track of the number of people you can say hello to and strike up conversations with. Some of those folks will obviously turn out to live right downstairs or four doors down the block. The "typical" New England personality is far more withdrawn than that of the part of the country where I grew up, but as is true anywhere people will warm to you once they get to know you.
Religious life in Cambridge is much in evidence, everything from Armenian Orthodox to Zen. Join a faith community if you're so inclined. Going to church/temple/whatever has always been an excellent means of launching acquaintances and - it has to be said - scouting promising spouse material.
Welcome to the 'bridge!