George Washington did battle with the British in Brooklyn , where he was loosing. When night fell, he and his men escaped across the East River to Manhattan.
He also did battle with the British in Manhattan where the British chased him and his troops through Harlem.
At some point I seem to recall someone set fire to the city.
There was also some sort of a fort in NJ for the Revolutionists in what is now called Fort Lee on the Hudson. There's a Museum there you might want to check ouy.