Yesterday, I visited the garden at the Bronx for the first time. I am very impressed.
Having both landscape architectural design as well as natural look. The Brooklyn Botanical Garden is nothing by comparison. This is a perfect location for a peaceful resting, studying, etc. Free admission on Wednesdays and Saturday mornings. Doesn't seem as crowded as Central Park or even the Brooklyn garden. The only drawback is that it's too far up in the Bronx.
So far, there are two waterfalls in New York City that I know of, one by one of Bronx Zoo entrances, another one, a very nice one, in the New York Botanical Garden. They are not big, but pleasant enough. I wouldn't consider Central Park's couple of mini-falls as waterfalls.