You may have difficulties finding an apartment for under $600. The only areas I have seen that low are bad sections of Providence, Central Falls or Woonsocket. I lived in Downtown Providence for a year, in a not so great section and my rent was $630/mo., but I hated it there and the management was absolutely horrendous.
It's possible if you just find a studio...but finding a 1 bedroom will be difficult. When I was looking to move out of Providence, I too was looking for a 1 bedroom apartment. However, no matter where I looked I couldn't find anything decent under $800/mo. Housing is very expensive here...so I had to move back home with my Mother for now.... I wish you the best of luck in finding what you are looking for :-). Wish I could be of more assistance.