Where I'm at that's about $1000/month plus health insurance. Minimum wage is $1700/month.
You could get cheaper, but you'd be far away from the actual city (at which point you might as well just live somewhere else).
However NYC as a whole has high sales and income taxes though. Including City income tax.
Brooklyn is where you live when you move to The City without a lot of money - like for grad school.
Rent is (probably) higher in Park Slope or Williamsburg though which are more "desirable" areas of Brooklyn.
I'm sure natives can chime in.