New York City has the highest percentage of green space of any city in the US? That has to be a misleading metric, including less inhabited areas way out of the city proper. If you're in Manhattan, the only green spaces are little square parks, tiny alley parks accessible only to people with children (lame!), and central park. The city does not feel "green" at all.
If you go to DC, on the other hand, all sidewalks are thoroughly planted with trees and shrubs and such, and there are many buildings with big lawns and gardens. DC feels much greener than NYC.
NYC != Manhattan. 1.6 million of 8.3 million New Yorkers live on Manhattan.
Traditionally good neighborhoods have lots of parks.
DC is very similar IMO. The through streetscapes were intended to be beautiful, which anyone who has seen Queens boulevard can tell you is not true of NYC. But at the neighborhood level, it's pretty similar.
NYC has absolutely massive cemeteries. I would be that they are counted in the green space though they don't have the kind of attractions that people typically associate with parks as they are densely packed.
There were at least a few dozen "pocket parks" within a 15 minute walk of my home. Juniper Valley park was a larger park about 15 minute drive/30 minute walk. Forest park was a little further.
D.C. is definitely more green than NYC. I think statistics might toss out the Mall and the Ellipse, which basically function as parks. Or they make other mistakes in counting, something like 90% of D.C.'s parks are controlled by some other group than the city park service.
This article claims that 96% of residents live within 1/2 mile of a park.
It turns out D.C. and NYC have almost exactly the same percentage of parks (19.4% and 19.5% respectively).
However, if you look at cities with lower densities, Albuquerque, San Diego and Virginia Beach all handily beat D.C. and NYC as cities with a high percentage of parks.
And later down you can see other interesting figures, like Acres per 1,000 residents (Oakland and D.C. come out on top while NYC comes out much lower (and not surprisingly the parks in NYC are packed full of people on nice days).
I think you're forgetting about the big parks, like Central Park, Prospect Park, and Flushing Meadows-Corona Park. You may not live close to them, but they take up a lot of space.
(To a lesser extent, there is also the Hudson River greenway, and the new Brooklyn Bridge park. These take up a good chunk of space too.)
If you go to DC, on the other hand, all sidewalks are thoroughly planted with trees and shrubs and such, and there are many buildings with big lawns and gardens. DC feels much greener than NYC.