New York City's most famous greenspace is Central Park designed by Olmsted and Vaux (pronounced Vox). But the city supports more than this (central) park. Here are several types of greenspaces to be found in the city:
Produce at the Union Square (14th Street) Farmers' Market
Another square, to the south - Washington Square Park
Spots of green on the balconies of the old Chelsea Hotel
Mid-block East Village courtyard
Gardens powered by steam at Cooper Union
I was absolutely thrilled to discover the Time Landscape (shown below), a patch of Manhattan woodland created by landscape artist Alan Sonfist in 1978. Learn more about the constructed woodland and the historical ecology of the neighborhood at the NYC Dept. of Parks and Recreation website.