I get a lot of emails from people asking for advice about moving to Boston, so here's my general advice. Let me preface this by saying these are my OPINIONS gained from my experience living in several different areas in and around Boston, spending time at friends' places and looking at countless apartments & houses in many more areas. Also, I have a budget that does not allow me to live downtown or in swanky neighborhoods like Beacon Hill, so my advice is for the thrifty sort.
First, get to know Boston's public transit system, the MBTA, usually refered to as "The T". Where you want to live should be convenient to a "T stop" because you definitely don't want to drive to work every day. See www.mbta.com for information. My favorite way to commute is on the Commuter Rail, as opposed to the subway; Least favorite is the bus. Commuter rail lines are depicted by purple lines on the MBTA maps. The subway lines are the Red (north-west=>south-east), Blue (east & north), Orange (north-east=>south-west) and Green Lines (west).
Fondest memory: Where I would live if I could afford it:
Newton Center, Chestnut Hill or Brookline Village (Green D Line)
Dedham or Needham (Needham Heights Commuter Rail)
Cambridge (Red Line) Arts, culture, good restaurants, pubs & history.
Where I have lived and liked it:
West Newton (Commuter Rail, Express bus or drive to Green D Line): Convenient to the Mass Pike, restaurants & shopping in Waltham, Watertown.
Roslindale (Needham Heights Commuter Rail or bus to Orange Line): Charming old-school Boston neighborhood. Great Greek food! The Arnold Arboretum nearby.
Medford (buses to Orange or Red Lines, Lowell Commuter Rail): Convenient to Route 93, 30 minute walk to Davis Square, Somerville, Tufts University.
West Roxbury (Needham Heights Commuter Rail, bus to Orange Line): Quiet, walk to restaurants, grocery store. Arnold Arboretum nearby.
Where I have spent a lot of time and would consider living:
Watertown (Express bus, bus to Red Line): Convenient to Harvard Square, great restaurants, Charles River bike path, shopping, convenient to Mass Pike.
Jamaica Plain (Orange Line): Great restaurants, pubs, garden shops, thriving arts community; Arnold Arboretum is right there.
Somerville - Davis Square (Red Line): Too many restaurants, pubs & entertainment to choose from, thriving arts community.
Wakefield (Haverhill Commuter Rail): Nice, social, suburban community with a pretty lake right downtown.
Melrose (Haverhill Commuter Rail): Lots of pretty, gingerbread Victorians.
Winchester (Lowell Commuter Rail): Charming old downtown area.
Places I avoid due to safety concerns (AGAIN, these are my OPINIONS. Please don't get mad at me if you disagree):
Revere, Chelsea and Everett are borderline neighborhoods in my opinion. There are nice places and not so nice places but I think the not so nice places outweigh the nice ones.