Providence's craigslist is pretty small. You can try that, but I think projo or the Phoenix would be better. And I would try to stay in or near Providence. Someone mentioned New Bedford, but if you live there, you aren't really experiencing living in RI. RI has it's own culture, and it's pretty neat. There is also a lot more to do in Providence than New Bedford.
I really think it's funny that $800 is considered expensive for an apartment. That's what I paid to live in Warwick. I won't even mention how much I'm paying now for my one bedroom in Boston!