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 more expensive them Boston in some parts. Somerville and Medford are decent, stay away from Chelsea and Everett. I would recommend against Revere. Brookline is too expensive for you, most likely. Newton is nice, but also a bit pricey. Heck, even moving to somewhere on the T (Boston's commuter rail) like Framingham or Worcester could work, because rents are far cheaper outside the city.
Hope this helps.