I lived for a time in a nice suburban community about 20 minutes south of Providence, and 10 minutes south of PVD. I'd definitely stay in the city, and the apartments around the universities would be the best bet. There are nicer apartments around the train station, but those probably are a bit more than 1000$ a month.

All of the suburban stuff is fairly family oriented, and most of the communities immediately surrounding Providence aren't that nice to live in.