Yes
You can drive in New York State with a valid driver's license from another state or country. You do not need to apply for a New York State driver's license unless you become a New York State resident.
What if I am a tourist and I have a driver's license from another country?
If you have a driver's license from another country, you don't need to have an International Driving Permit, but it is useful. The permit verifies in multiple languages that you have a valid driver's license. Police officers who cannot read the language of their foreign driver's license will be able to read the permit.