What is the land of the law mean inNY state to me ifI was not at fault in an accident as stated in a police report, and other driver is unlicensed?

It is irrelevant that the at-fault driver had no drivers' license.  The police will likely give him a citation for that and he'll have to deal with the court.  If the accident was his fault, he is responsible, but under the laws of ny, if you have your own insurance, your insurance should cover your property damage.  If you do not, you can go after the other driver's insurance if he has any, but you are not likely to get anything since he a)is unlikely to have any and b)ny is a no-fault state, so your insurance should be paying.  If you were injured, you can present a claim to your own insurance.  You can only make a claim on the at-fault driver's insurance for your injury if you have suffered:

• A permanent loss of use of a body organ, member, function and symptom.
• A permanent consequential limitation of a use of a body organ or member.
• Significant limitation of a use of a body function or system.
• A medically determined injury or impairment of a non-permanent nature which has prevented you from performing substantially all the material acts which constitute your usual and customary daily activities for not less than 90 days during the 180 days immediately following the accident

So, a bump on the arm wouldn't qualify, but a broken arm would.  Hope that helps.