In New York you will receive 2 points on your driving record if you are convicted of an improper / illegal U-turn.
If a no u-turn sign is posted at an intersection it normally means that no u-turn can be made onto the main street or any side service road if it means making a u-turn in your vehicle.
The NYS Vehicle and Transportation (VAT) laws, section 1161 is termed U turns in certain areas prohibited. Here it states that no motor vehicle shall make a U turn upon any curve, or upon the approach to, or near the crest of a grade, where such motor vehicle cannot be seen by the driver of any other motor vehicle approaching from either direction within five hundred feet.
If you were cited for making an improper U-turn in NYC but want to fight the ticket then you may want to take pictures of the intersection if you found the U-turn signage to be confusing or misleading to see if it helps your case in court.