Market rate for something like dr_ described (only a few blocks to subways and Central Park) is probably ~$2400 for a studio, ~$2900 for a junior one bedroom, ~$3200 for a one bedroom, assuming not poor shape (at least dishwasher) but not luxury. Probably an elevator (there aren't many walkups that close to the park). More for a doorman.

You can get cheaper if you go significantly towards the rivers (for example west of 10th ave) at the cost of a more industrial feel and longer walk to transit and the park. Those buildings would also be more walkups.

Perhaps you can find a deal as a roommate if you know people as one of the other posters said, but if you're looking for a whole apartment and don't have connections that's the ballpark.

Also, it's very hard to get a sense of how cheap the market goes from looking online because chances are there's a catch or the listing isn't real. NY listings tend to lie outright (1BD is actually a convertible studio, etc).

Source: lived a few blocks from Columbus Circle last year.