First, as stated by others, don't do it! If any way around it, stay out of N.Y. state. But, if you must:
DO NOT BRING A HANDGUN INTO THE STATE OF NEW YORK WITHOUT FIRST HAVING A LICENSE FOR THAT HANDGUN!
Following is a copy of an FAQ from the N.Y. State Police website concerning this issue:

FAQs - Relocating to another state or county
Q - How does the law apply to licensed individuals from other states who move to New York and wish to posses their handguns here?
New York State currently has no reciprocal agreements with any other states and does not recognize any other state's licenses. It would be unlawful for an individual to move to New York State and possess handguns in the state without first being licensed by the county in which the individual will reside.
There are two options for individuals already in possession of handguns in their home state.
[ul][*]They must either leave the weapons in the possession of an individual in their home state who may lawfully possess them until such time as the owner can legally possess them in New York State, or[*]They may leave them in the possession of a licensed gun dealer in their home state who would be willing to hold them until that individual can lawfully possess them in New York State. [/ul]

In either case, the weapons can only be lawfully brought into New York State via a licensed dealer in the home state shipping them to a licensed dealer in New York State from whom the owner may take possession.
Weapons personally brought into New York by the owner would result in forfeiture of the weapon and possible criminal charges brought against the owner.
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If you take any handgun into N.Y. without first having the license for it you can, and likely will be, charged with a FELONY. At that point you can kiss your RKBA goodbye - forever.
(Even New Jersey is not as bad as N.Y. on possession of firearms.)
If you're moving to New York City, just hang it up/forget it, and sell your guns first.
Here's a link to that FAQ above: http://www.troopers.state.ny.us/FAQs/Firearms

Also, here's another useful link, the NRA's website on gun laws which includes info. on each state. It's usually pretty accurate, but always double check it: http://www.nraila.org/GunLaws/Default.aspx