These hotels are all within 5 minutes walk of the NYU Game Center.
The following hotels are a little further out, but still very near the center:
Affordable Accommodation Options
AirBnB allows people to sublet rooms, apartments, or just a sleeping space in a shared room. Prices as low as 30 dollars a night are feasible, but you might be sleeping with strangers in the same room. The site usually offers descriptions and images of how your accommodation will look, but one should be careful to read all the details to avoid surprises. Checking out reviews of previous guests is also recommended.
Also, the prices drop as you get further away from downtown Brooklyn. Have a look on google maps to see how good the public transport will be from your location. The existence of a direct subway line can make a huge difference in travelling time.
While AirBnB is probably the largest provider of P2P rentals, there is a range of competitors, many of which are active in New York. For an example list see:
There is an active couchsurfing community in New York, and if you are lucky someone might be willing to let you stay in their place for free. Similar considerations to AirBnB apply regarding reviews and travelling time.