I always book early for New York as they fill up pretty quickly, generally I book with someone like Hotel Connect or last minute.com as they offer the lowest prices.
Its easy to get around in NY though so don't be persuaded by location the subway is cheap and runs late to get you from point to point.
Hi, there many hotels in new york waiting for you!
If you want the cheapest, try "Chocolat Hostel", it is about $22/night
Of course, it is not the best one for you , you can find some better hotels that can meet your requirement and can also save your money. http://hotelally.com can search all the best hotel booking sites at once and can give you the best answer, you can try it