NY State is one of the most difficult states to file and obtain a CCW, IMHO. They require a 6 month waiting period, multiple personal and business references, FBI checks, and the hardest one a valid need of use for the possesion / carrying of a firearm. During my 19 years living in NY my father was involved in Law Enforcement. Even after he retired as Chief of Police of a town in Upstate NY he was required to go through the application process again. He obviously had an easier time due to his past but still went through the entire process. My brother also applied, he never had any criminal record or anything that would normally bar him. They would not grant him the CCW based on not having provided a reasonable need for the carry permit.
As far as NYC is concerened the regulations get even harder. They are considered a non carry city. Law enforcement and certain other peace officers can carry. Even people with carry permits good in the rest of NY State are not allowed to carry in NYC without a written pre-authorization from a governing body in NYC (NYPD, County S.O., or The NY State Troopers). This approval is again given on a case by case basis. Usually very hard to get even for a short trip. Some of the minor details may have changed since 9-11 but most should be very accurate.
My advise is to stop into one of the NY State Troopers substations in the state and talk to the Commander on duty. They are always very helpful and by far are experts on the gun carry laws of NY.
Hope this helped, if you have any other specific questions PM me and I will get in touch with my father or a good friend from HS that is a Trooper there.