You can definitely find a decent place in Boston in the $1000-$1200 price range, even in a neighborhood like the Fens. I know because I used to own property there. There are cheaper places in Allston, Brighton, South Boston, East Boston, and Charlestown. Some parts of Roxbury and Dorchester are inexpensive, but they wouldn't be my first choice. Same with Jamaica Plain. Where exactly is your gf going to work, the financial district? Commuting and excessibilty to your workplace should be one of the main factors in considering where exaclty to move.
Suburbs like Cambridge are great, but even