While browsing the Museum of the City of New York’s Byron collection online archive, I came across the photo from 1903.
Interestingly, instead of going by the park’s real name, it’s mysteriously labeled the “German Play Ground.”
Must be Tompkins Square Park, which was heavily German at the time—so much so that the neighborhood was known as “Kleindeutschland,” or Little Germany.
Of course, lots of neighborhoods were German, such as Bushwick, known for its breweries. But here, I think the winding paths and benches give it away.