Wikipedia has this to say about Untermyr Park:

Untermyer Park (also known as Untermyer Gardens, previously part of an estate known as Greystone) is a historic park of 43 acres, situated in Yonkers, Westchester County, New York, just north of New York City. Untermyer Park is on a hillside above the Hudson River and features a rock garden, a “Grecian garden” (actually a Persian Paradise garden), a small Grecian-style amphitheater, a classical pavilion, pergola, statuary, and a view of the river.
The Untermyer Gardens were developed during the first 40 years of the 20th century, when the area now enclosed by the park was part of an 150-acre site that was the estate of the lawyer and civic leader Samuel Untermyer.
Greystone had previously been owned by defeated Presidential candidate Samuel Tilden. Untermeyer purchased Greystone when Tilden died in 1899; when Untermyer himself died in 1940, his plan had been to donate the whole estate to the Nation, or the State of New York or at least to the City of Yonkers. Eventually the city of Yonkers agreed to accept part of the estate; this parcel of land, which was the core of the gardens, was renamed Untermyer Park in his honor. The Park was added to the National Register of Historic Places in 1974.

I’ve subsequently discovered that there’s more to the park than I realized. When I went it was still very cold so I didn’t hang around for long. Hopefully I’ll be able to go back one day when the weather is warmer.

I’ve read that they don’t like you to take pictures inside the walled garden. However, when I went nobody was around. If you go, it’s probably a good idea to take a small camera though – something unobtrusive.