You can also try Jersey City, NJ (Grove Street area is cheaper than Exchange place/newport). Try to be close to the PATH train ($1.30 to the city and pretty fast). You might be able to share a small 2 BR for $700/month.
I don't recommend NJ that much because: 1) once you use PATH you may still have to use NYC subway to reach your school or get arround. double charges. 2) there isn't much chinese supermarket/restaurant in NJ.
However, NJ is overall more clean than Queens/Brooklyn.