Westchester or Long Island
To get your license faster, you can travel outside of the city and apply to the clerks office in Mamaroneck, NY. You must have an original birth certificate and a government issued photo ID. More info at Mamaroneck City Clerk
Its a 42 minute train ride from Grand Central Terminal and a short walk to the clerks office from Mamaroneck Station. The train cost is approximately $19.50-$25.50 round trip per person. You must first call them to schedule an appointment.
Babylon Long Island Town Clerk is open as well for licenses. You must have a birth certificate here as well.
Take the LIRR to Lindenhurst Train Station from Penn Station and then a Taxi to 200 E Sunrise Highway Lindenhurst, NY 11757