cma has given you a very accurate description of the process..."The process varies by county, and so do the odds of getting a carry permit. Luckily for me, my local county (otsego) elected a pro-gun sherriff, and he prefers issuing (his own words)carry permits.

There were never truer words about the process in NY - it does vary significantly from county to county as to whether you will even be approved or not. This is entirely up to the discretion of the County Judge!
If the Judge doesn't believe people should have pistols, he can deny a permit for no real reason. he can also issue a "restricted" (hunting & Target) permit, even though there is no provision for such a thing in NY State law. Likewise, there is no provision in NY State law for a "concealed" permit. IF the county issues you a carry permit without any restrictions, you can carry the thing concealed or openly, as you wish. If the permit is restricted to premises, you cannot carry it at all!