The Nelsons arrived in San Juan on Saturday for a weeklong vacation belatedly commemorating their 51st wedding anniversary. Crews found them the next day.
Cuomo vowed to send NY aid to the devastated islands.
The Caribe Hilton reassured them that if they stayed, they would be safe with the resort's backup generators and water supplies, he said.
"New York is home to more Puerto Ricans than any other state in the country, and our hearts break for our Puerto Rican brothers and sisters as they begin to rebuild after the unimaginable devastation of Hurricane Maria", Cuomo said in a news release Thursday night.
"This is all of us", said Isa. "We fell asleep to it, when we could sleep", said Dawn-Michele Moros, 50, of Greensburg, on watching the hurricane approach her parents' vacation spot.
Eventually, the family were located more than 50 miles from their original location, near the island of Vieques.
The Coast Guard in Miami received an alert and a distress call stating that the boat - the Ferrel - was disabled and adrift in 20ft (6m) waves and 99mph winds on Wednesday. They later lost contact with the vessel due to the weather.