hahaha, depends on where you want to live.
if you're looking to live in manhattan proper (i.e. below 96th street), then a decent studio will cost you at least $1400/month on the UWS. if you're willing to live between 125-145th street, then you could probably find a multi-bedroom where your share of a room will be about $800-1000/month. but if you're willing to live in harlem, why not live in washington heights?
imo your best bet is to do columbia's housing. that way you're right on campus and you're spending $600-700/month for a pretty large room compared to the rest of manhattan.
*real estate brokers are SHADY! they leave a bad taste afterwards. also, even if you don't pay a broker's fee (usually 1.5x rent), they'll hide the cost in higher rent anyway. do NOT trust those ads in craigslist that advertise apartments that are too good to be true, they don't exist. they're only meant as a lure so they can show you all the other options. it's actually worth it to pay a higher price and the broker's fee so that you get better service and someone reputable.
**my friends found a really awesome apartment in midtown. it's a walk-up, 3rd floor, 3-bedroom where each pays approx ~$1300/month each = $4000/month total. great living room, lots of space, i was amazed when i saw it! so you can find a good place, especially if you have friends who you can find a multi-bedroom with. when i was in new york i lived in a door-man building w/ a roommate, $1400/month each or $2800/month total to share a 1-bedroom! i lived in the living room... damn that was expensive.