At 15 US$ * 50h/week * 48weeks/year = 36,000 U.S. dollars living at 515 West 52nd St., New York, NY 10019 a 2bed 2 bath is 5,265 / month, but it's a block from central park. Split that 4 ways and your rent is 1,316 but utility costs are low. (There are cheaper places to live around there, but these are fairly nice apartments.)
15 US$ * 50h/week * 48weeks/year = 36,000 U.S. dollars, I had a single apartment at 1050$ per month and a car while making 38k so I know it's reasonable to make it like that. Now having a wife and kids on that is not going to happen in that area but NY is more a place for the young or the rich.
Edit: 36k = 28k take home so about a grand a month after rent.
PS: Trying to make it on 15$ an hour in NY, NY might seem stupid, but a good internship can be worth it.
You are also picking the most expensive place to live. A big 2 bed 2 bath duplex with a porch is $2100 up in Harlem (near 125th). That's $525/month split 4 ways, also a very nice apartment (3 blocks from the 4/5/6 train).
If you work between lower manhattan and 33rd st, you can live in Jersey City and rent a huge 3 bedroom for $1500 ($500 split 3 ways). Commute time is 15-25 minutes.