This is good information. I was just there last week but we also had a car service ready for us. Just Google "New York Car Service" or go to this website: http://www.citidex.com/899.htm
Be sure to scroll all the way down the page - through "TelAviv Car & Limo" - that happens to be the service we always used when I lived in the city simply because we found them to be very reliable.
You will see there are many car services in NYC (it is a city where few people own cars). Prices should be pretty standard, also.
I suspect that if you planned to get off later, say 10:30 or 11:00, that there would be a trickle of taxis from the early arrivals of people coming aboard. By 1:00 it is the opposite, nothing but taxis and no riders.