Craigslist is probably your best bet for affordability and a good amount of listings. Have you seen
HousingMaps It's a great Google Maps and Craigslist mashup for the apartments and housing section. I found a few great apartments that way here in Providence. It makes searching through the Craigslist ads a whole lot easier, though it only works if they give an address or intersection in the ad (most do).
Rhode Island apartments and houses for rent | RI apartment rentals homes and lofts is another site that might be useful. If you're looking for an apartment to rent, I'd probably stay away from a real estate company.
If you're going to be attending or working at RISD, they might also have an off campus housing office that can help you find a place. Brown's off campus housing office has their listings available for anyone to see
Auxiliary Housing at Brown University: About Us. With Brown being so close to RISD, it might be helpful for you as well.