It WILL hurt your credit score and it is not advised unless you are absolutely upside down loan to value and MUST move. If you are handling your payments and can stay where you are, you might look into a refi to lower your interest rates.
If you absolutely have to sell, the short sale is the least of the evils and YES it will hurt your credit. It does not matter whether you are selling in NY or anywhere else.
If this is your primary home, the lender will "forgive" you the money owing, but you will definitely not be able to get any $ out of the sale.
Typically, when funds are received from a short sale, the bank may still hold you responsible for the balance. There are just too many questions to ask here on an open forum to be able to help out. There are plenty of options which could be looked at to avoid this.
Terrence Charest, e-Pro