Belvedere Castle / Turtle Pond
Belvedere Castle sits atop Vista Rock, north of The Ramble (around 79th Street) and was originally designed by Calvert Vaux as an observation tower to overlook the old reservoir (now the Great Lawn). It was built in 1869 on the site of a former fire tower. The original plans included a second, two-story structure just to the West of the castle, but cost overruns prevented further construction. The castle is built with the same kind of schist as Vista Rock (giving the impression of the castle rising out of the hill) with light-colored granite trim from Quincy, MA and roofing slate from Vermont, Virginia and New York.
The word "Belvedere" is Italian for "Beautiful view", so, presumably, the building was not named after anyone named Belvedere.
In 1919, the US Weather Bureau moved their observatory from the Arsenal to the the castle, closing the formerly open-air structure for offices and altering the shape of the turrent to house meteorological instruments. The observatory was automated in the early 1960s and the building was dormant until 1983 when the Central Park Conservancy restored the original turrent and pavillions and converted the castle into a visitor's center. The Henry Luce Nature Observatory was added in 1996, providing interactive nature exhibits and distributing bird-watching kits. (reference)
Just below Belvedere Castle and to the south of the Great Lawn sits Turtle Pond (also known as Belvedere Pond), one of many smaller bodies of water in Central Park. It's decline paralleled that of the Great Lawn and its renovation was included in the Great Lawn improvement project in the late 1990s.