I suggest that you use public transportation to get to and from the airport -- traffic is bad and tolls/parking is expensive.
Most of the nicer places are quite expensive (Back Bay, Beacon Hill, Cambridge, Newton, Brookline, South End). I think you might find some cheaper places in South Boston. Charlestown has some very expensive parts (waterfront) and some not so nice places (near the public housing projects). Lynn and Everett are cheaper, but can be a bit dodgy. East Boston is close to the airport (good and bad, that) and was less expensive, but prices are increasing.
Somerville and Medford are traditionally a bit more affordable, as is Arlington.