Landing at Newark Liberty International Airport (EWR) just across the river in NewJersey may be another option since it's served by close to 20 international carriers.
Exempt from the extra scrutiny are visitors entering by land or those from 28 countries (mostly in Europe) that don't require a visa for short-term visits.
Travelers along Canada's Highway 401 can cross the St. Lawrence River from Cornwall, Ontario, to Massena, New York; from Prescott, Ontario, to Ogdensburg, New York; from Ivy Lea, Ontario, to Alexandria Bay, New York; and by ferry from Kingston, Ontario, to St. Vincent, New York.