score:3
Depending on how you count it, there's somewhere between about 550 and 600 hotels in New York City.
Doing a booking.com
search for "new york" for a random date next month, and selecting "New York City", shows "520 Hotels found in New York City".
A similar search on Expedia finds 502 hotels. hotels.com
finds 685 hotels - but then tells me that 152 of those are not available for the dates I've selected (a pattern which seems fairly consistent regardless of what dates are selected).
As far as price, hotel prices in New York can vary significantly, and especially on weekends you can get some good prices (I stayed at a great hotel in Manhattan on Friday for $150+tax), but at other times it can be very expensive - especially in Manhattan.