NYC has always been a very tight car rental market. Even in times when weekends were always dirt-cheap, NYC would still end up being $60-70/day or more. The main reason is that most agencies prevent you from using coupons at the three airports and the Manhattan locations. So the ubiquitous "3rd Day Free" stuff we all like to use on weekends doesn't work there.

I did a four-day weekend rental at LGA two years ago: two National Free Days (the ones you get for every 6-7 rentals) and two Hertz ZE1 Free Days (using their points). I had to do a car swap in the middle of the trip but it saved about $400 including taxes. Fortunately we were only 40 minutes away in Connecticut and could do the swap early on a Sunday morning.