Live in NYC, but borrow/drive a car in NJ…what type of car insurance do I need and for which state do I need it for?

Auto insurance follows the car. If the car is owned by another party, and they allow you to use it, the car is insured by the owner. The car can be used in any state in the US and the insurance from NJ would be valid. However, they need to be sure there is no limitation on their policy that requires any driver be listed on the policy. This is not a standard requirement, but is on a few policies. Have them check with their agent or company.It is not required that you be added to the policy unless you become a frequent driver. That can mean different things to different insurance companies. Nothing needs to be done at this time, but if you have an accident, the insurance company may require that you be added to the insurance policy and rated for on the policy. This could increase the rates for the owner of the car, depending upon your driving record. If you do not want to be added at that time, the insurance company can exclude you from the policy.