New York City has five "boroughs:" Manhattan Island, the Bronx, Brooklyn, Queens, and Staten Island.
When we think of New York, we usually think of Manhattan. Manhattan is an island. It's surrounded by water: the Hudson River on the west, and the East River on the east. I imagine that those are the "blue areas" you are seeing.
Most of the famous and iconic places of New York are in Manhattan. Manhattan includes Wall Street, Times Square, Central Park, the Empire State Building and other skyscrapers, the United Nations, Broadway and its theaters, the Metropolitan Museum of Art, and so forth, are all in Manhattan.
Manhattan Island is connected to the other boroughs by a number of big bridges and some tunnels. The bridges are long. There are pedestrian walks on some but not others. Pedestrians can walk across the Brooklyn Bridge, but there is no way to walk across the long bridges that cross the Hudson River to New Jersey.