I don't know what a NYCE ATM card is. If it is on one of the big networks, it will work. Maestro, PLUS, and Cirrus will work, and I'd bet there are other networks as well. It is my understanding that VISA or Mastercard branded cards are on an international network and therefore will work (there may be exceptions, check the network logos on the card).
On the off chance you run across a machine where your card doesn't work just go to another machine. I've had this happen once or twice in years of travel (no idea if it was a faulty machine, a network issue, or other problem, but it was resolved by simply walking to a different machine).
You do need to call your bank to notify them you will be traveling, so they don't freeze the card on fraud suspicions.
A PIN number is not needed for chip-and-signature cards at manned locations. That is, anywhere a person is running the card (store, restaurant, inside a gas station). Their machine just prints out a paper for you to sign. The only place you may run into difficulty is at automated machines, like gas pumps or ticket kiosks. Sometimes these require a PIN, so it's possible you couldn't use them - there's usually a counter with a person and you can pay there instead.