Basically, a room in a two bedroom apartment is worth approximately half or a little bit more than half of the total rent. Two bedroom apartments cost around $3000 a month and higher (I suppose it's possible you could find one for $2500). So bascially if you have a 'room' in an apartment like that, it will cost you $1500 a month.
I have seen apartment shares in Manhattan listed for lower than that, but they tend to not go below $1000 for a room.
The best place to see what shared apartments are going for is on craiglist at
new york city rooms & shares classifieds - craigslist then click on the image box so you only see ads with images and then hit search.
I highly suggest you look in Brooklyn or Queens or the Bronx instead of Manhattan with that budget.