Anywhere in midtown, village, it's going to be at least 1600 for a studio for the most part. Just spent a month looking for a place in greenwich village. And it's hard to find a place without using a broker, who's going to take 15% of the annual rent (almost 2 months of rent) as a broker fee.
You'll find that 95% of the ads are fake just to get you to call the broker listed, or are mislabeled as "no fee". But if you get lucky, you can find something. Padmapper.com (no connection to me) puts a nice googlemaps interface onto craigslist as well.
Edit to add:
When you get into the higher price ranges, and start looking in doorman / elevator buildings, it gets a little easier since you can deal with the management company directly. but that's like ~2200 and up or so probably.