This is sort of cheating because I love finding deals.. its sort of a hobby for me. I am registered with obitz, vayama, kayak, priceline, hotels.com, statravel, besttravel, cheaptickets.com and expedia.com (even more im sure).. I love that stuff.
To find the cheapest ticket I always go to priceline (they let you bid for your hotel/flight/rentalcar) because I've used them before and like the simplicity of finding cheap anything.
On initial search with most of my favorite sites, I got about 180 to 200 for a good 3 to 3 and a half hotel on the island (walking distance near times square) for July 31 to August 21.
BUT! I know that priceline will yield better results when you bid for your own price. They let you specify how low you are willing to go on stars, which area generally you would like the hotel to be and a price.
You have to enter your credit card information before you actually know which hotel youll stay at or even if you got the deal but usually if your not asking for a ridiculously low price, itll go through. Usually I bid a little less than half off the published price.
Generally, you can learn how to get the cheapest flights and hotels by adjusting the days of the week, maybe not going in a peak time of the year and by trying regional airlines.