Finding a decent true 2 bed room apartment in Manhattan will cost you $4,000 too.
Even ignoring north of 96th street (which, check a map, is part of Manhattan) there are plenty of neighborhoods where you can find a two bedroom for $3k or less. Yorkville, Chinatown, far LES, parts of alphabet city, the far west 30s, and probably others I'm not familiar with.
That you could say such a thing says more about you than the rental market.
See: http://newyork.cbslocal.com/2013/07/10/average-new-york-city...
Oddly, Brooklyn and Queens were not cheaper.