Yes you can claim unemployment from New York but it's better to register with NJ now as you have to do it later on. Different state has different laws, so the amount of money can vary.
If You Worked In New York State But Live In New Jersey Can You Collect Ny Unemployment Benefits Or Can You File In Nj?
I think if you are an American resident or you are going to be then you need an Ez pass login https://ezpassny.net in order to move around the country easier. After all, it's much more convenient to pay via one digital platform than having the current system.
Ny unemployment is very low,I living in nj I need to apply for unemployment in nj is better.