I did this last summer and I found an apartment in Murray Hill which I shared with another Adler student. It was only 2000 for the whole time, and I had to pay 1000.
As for food, you just have to budget. Get food from Gristedes and make your own food! It's fun and you learn how to handle yourself.
I totally suggest it.
"When you wish upon a star, you just might become one."