Register the car in NJ. Insurance is likely cheaper then anywhere in NYC. Now a story. A friend of mine had a car registered in NJ, but for some strange reason, the insurance company issued him a NY policy despite him telling them that he moved to NJ and switched all his paperwork (license, car registration). The insurance card even listed his NJ address.
Long story short, he got into an accident and the car was totaled with injury. The insurance company tried to weasel out of paying due to the policy being in the wrong state. The court said otherwise and made them pay up because he notified them of the policy change and they screwed up issuing the policy. Its not a hassle you want to deal with.