I've looked into this extensively.
There is a wide variety of housing options, and a concomitant variety in price. The highest end is an absolutely stunning new-construction highrise with floor-to-ceiling windows, marble baths, hardwood floors, 11' ceilings, spacious bedrooms, etc. The most expensive units in that building are 3-BRs running at $4300-$5000 a month (which is way below market price).
The cheapest option would be a studio apartment in the older buildings, which runs at $1400- $1700 a month. That is deducted directly from your hospital paycheck so you don't have to worry about remembering to pay rent.
If you're from out of town you might find that shockingly high, but the going rate on the UES is much, much higher.