Where is Cheapest (yet safe) place to live in or around NYC?

I'm moving to new york soon. I want to pay under 900 a month for a one bedroom/studio. I don't mind being a few miles out of the city just so I have easy access to get there. I was looking at some on long island,but I'm not familiar with the area so I'll need advice on that. Most of the cheap ones coming up were in the Bronx and Harlem... (no thanks). What are some other surrounding areas? Any best kept secrets out there? =]