I can't believe nobody has tried priceline---its a very good way to get a cheap room.
For example, a good friend of mine is staying in the Sheraton towers tonight (via priceline) for $69.00 before taxes...not too shabby 🙂
Expedia.com works okay too, you have to pay more, but you actually receive a choice. I am lucky, I have keys to two of my friends' apartments in the city, so for me its easy.
As far as where to stay, the train can take you wherever around the island, so don't fret if you're staying downtown and are interviewing at columbia--just take the A (express) train uptown and you could get from downtown to 168th street in less than 30 minutes.