While New York has many beautiful and inviting bodies of water, unfortunately many are off limits to seaplanes.
In Eastern New York, the Hudson River is open but salinity, traffic, and water conditions preclude operations until you get north of West Point. There are many reservoirs around the NY metroplex that are off limits. The canal systems to the north are off limits as are most of the lakes in the Adirondack Park. Lake Champlain is open and has many places to check out. The lakes that are open are highly sensitive to invasive species and many require permits and/or dealing with multiple layers of jurisdiction. Check the Water Landing Directory often.
Central New York has fewer bodies of water, but tends to be more open to seaplanes. The Finger Lakes are open, but be careful about the canal systems that connect some of them with Lake Ontario, as all canals in New York are closed. Western New York has the Great Lakes and Lake Chautauqua that are open, but beware of winds and surface conditions on the Great Lakes.