Where you would want to live should depend on your age, whether you're married or living alone. etc. But since it sounds like you're young and single, I would highly recommend living somewhere not too far out, with good access to public transportation -- the T (subway and streetcar system) if possible, or else the commuter rail. Boston is a real walking town and there are tons of things to do there (music, movies, restaurants), lots of educated young people, interesting neighborhoods. It's terrific to have so much at your doorstep. I lived in Boston about 15 years ago and I know it's gotten more expensive, but as a student town there should be housing options for somebody with an actual salary!
I eventually got tired of Boston and moved back to New York City. For a big, cosmpolitan city it's very tribal -- people tend to cluster together by neighborhood, and it will probably take you awhile to get a feel for things. Often it feels like an overgrown college town -- I believe that there are about a quarter million college/university students in the metro area! But it's definitely a city with an exceptional amount to offer compared to just about anything but the big leagues (New York, London) and I'm not sorry I spent to time there.
Also, the city itself is ringed by old towns that never got incorporated into the city proper but are very urbane -- Cambridge, Brookline, Newton, etc. Since Natick is west of Boston, it might make sense to look at the neighborhoods in that direction: Allston, Brighton, Brookline, etc. Cambridge is probably the liveliest spot; the adjacent towns of Somerville (more blue collar) and Arlington (more suburban and affordable) take some of the overspill.
Good Luck!