You should give Rumford a shot. My wife and I lived there for a few years (at 400 Pleasant St) before we bought a house. It's not easy on the eyes, but it was cheap and it's a hell of a lot better than living in the bucket. It's just a short ride to Prov and Seekonk. Looks like a 1 bedroom goes for $1295, upon a fast google search. Good luck.