Anyone can rent a boat in New York State.  You do not need a license to rent a boat.  According to the New York State Parks Department: 

“If you are at least 18 years old, you may rent without completing a course. The livery must demonstrate how to properly use the boat before renting it. Persons under the age of 18 may only rent a motorboat if they hold a safety certificate.”

In Kingston, on the Rondout Creek near the Hudson River, Hudson Valley Water Sports Rentals – Hudson Valley Water Sports (hvwatersports.com) has everything from water bikes to kayaks to jet boat rentals and guided tours.  

While a jet boat will get you where you’re going fast, a simple kayak is plenty to enjoy the boating experience on the river.  Hudson River Expeditions offers kayak rentals in Beacon, Peekskill, and Cold Spring.  All three locations are accessible by Metro North.

Saugerties Marina in the Northern Hudson Valley has pontoon boats for rent, with or without a captain in this beautiful scenic and quiet stretch of the Hudson River.

There are also dozens of boats available to rent, with or without captains, through Boatsetter.com and the Boatsetter app.  Boatsetter is like Airbnb, but for boats.