Or try the subways!
I see that you're from a place where the subways do not run all night long...
For a cheap way to spend the night, and see the city at the same time, and see interesting people, try touring the city by subway overnight!
A $2.00 fare will allow unlimited subway riding as long as you don't exit the turnstiles. And the Staten Island Ferry runs all night - cost = $0.00.
This is not as dangerous as it sounds.
Or for more luxurious digs, try the Long Island Rail Road.