It is good news for you that the hit and run driver was found and admitted to being responsible for the damage so you can now file a claim with the at-fault's insurance company. As for penalties for the hit and run driver, first in New York leaving the scene of an accident involving property damage is 3 points on the person's driver's license.
Section 600 of the NYS Vehicle and Traffic Laws addresses leaving the scene of an incident involving property damage without reporting it even more. It states that doing so is a class B misdemeanor punishable by a fine of not less than $250 nor more than $500 in addition to other penalties provided by law. This likely means he will need to go to court for the violation. A class B misdemeanor can be given a maximum sentence of up to 90 days in jail.
If after your car is repaired you are in need of New York car insurance you can start getting a quote here with us.