One thing I like to do in US cities I visit is look for buildings and facilities that had been built as part of the Works Progress Administration (WPA) during the New Deal, and New York City has plenty of them. Hundreds of projects were things like sewer and road improvements so they are not exactly sites you want to visit, but there are also a lot of buildings, parks, and other recreation facilities built through this New Deal program and still in use today.
About a dozen large swimming pools were built, a life saver for those living in hot tenement apartments.