In a map of the Republik van Nieuw Nederland, Paul Burgess imagines that the Dutch never gave up their New World possessions and a republic formed centered around New Amsterdam.
New Amsterdam never gave way to New York. The Dutch kept the whole of their North American colony out of the hands of the perfidious English, in fact. New Netherland today constitutes a thriving Republic stretching from the Atlantic coast to Quebec, dividing New England from the rest of the United States.
See also Melissa Gould's map of Neu York, which imagines Manhattan as a post-WWII Nazi possession.