Olmsted and Vaux’s “folly” (or fantasy building), this turreted castle sits atop the second-highest elevation in the park. Inside is a nature observatory with good rainy-day activities for children. In front of the castle is the Delacorte Theater, where the famed Shakespeare in the Park is performed, a star-studded and free evening of theater staged in the summer months only. If you decide to take in a show, know that you could end up spending 4 or more hours standing in line to get tickets; they’re passed out at 1pm in front of the theater, but depending on the popularity of the show, crowds have been known to show up hours before that, and even camp overnight at the gate to the park. From Belvedere, you’ll also look down on the Great Lawn, which has gone through a number of incarnations, first as a reservoir and later in the 1930s as “Hooterville,” the shantytown where hundreds of homeless families lived out the Depression. Today it’s most famous as a concert space: Simon and Garfunkel reunited here in the early 1980s in a widely televised concert.