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New York's only statutory rental age is for personal watercraft and specialty prop-craft: Navigation Law §73-a bars a livery from renting one to anyone under sixteen, and in the same clause requires genuine proof of identification and age plus compliance with the boating safety certificate rule in section 49. A personal watercraft renter over eighteen may skip that certificate only where the livery keeps them within five hundred feet of the agent assigned to supervise, on a clearly marked craft.

Operating age is separate. Section 49 sets ten years for a mechanically propelled vessel and fourteen for a personal watercraft, each with a certificate; a personal watercraft operator may instead be accompanied by a certificate holder over eighteen. Rental companies set their own minimum age.

Source: New York State Office of Parks, Recreation and Historic Preservation (nysenate.gov)

Yes, but New York calls it a Safe Boating Certificate rather than a boating license. The state generally requires recreational operators of motorized vessels to complete a state-approved course and carry the original certificate, including for personal watercraft. Operators of other motorboats must be at least 10, while PWC operators must be at least 14. Renters age 18 or older may operate a livery motorboat without a certificate after receiving basic instruction and safety information; a rented PWC may be operated without one only within a marked area near the livery. Renters under 18 need a certificate, and no one under 16 may rent a PWC at all. Course graduates receive a temporary certificate valid for 90 days. Valid U.S. Coast Guard operator licensees are exempt. New York State Parks administers the program.

Source: New York State Office of Parks, Recreation and Historic Preservation (parks.ny.gov)

From New York City, aim for Upper New York Bay, the Hudson River, the East River toward western Long Island Sound, or Jamaica Bay. Upper Bay is open harbor water between The Battery and The Narrows, with Governors Island at the East River entrance. The East River is a tidal strait; Hell Gate has strong currents and heavy traffic, while western Long Island Sound is more protected. Jamaica Bay, reached through Rockaway Inlet, is a marshy pleasure-boating area with dredged channels and anchorages near Canarsie Beach. For a Queens launch, the concrete ramp by World’s Fair Marina accesses Flushing Bay, which is mostly shallow outside its marked channel.

Source: NOAA Office of Coast Survey (nauticalcharts.noaa.gov)

Good day-trip destinations from New York City are City Island, Great Kills Harbor and Atlantic Highlands Municipal Harbor. City Island sits between western Long Island Sound and Eastchester Bay, with marinas and popular seafood restaurants. Great Kills Harbor offers visiting boaters a marina beside a Gateway park with a beach, fishing areas and trails. Atlantic Highlands Municipal Harbor welcomes visiting crews with transient berths and harbor restaurants.

Source: City Island Nautical Museum (cityislandmuseum.org)