Columbia University

This beach is a pleasant place to relax. The water is safe enough to swim in, but it's not the best you can get (you'd get a better deal down the Jersey Shore or on Long Island). The boardwalk, one of the longest in the United States, is great for running or biking.

See the Rockettes, another show, or just tour the famous Art Deco masterpiece.

A historic site, not least because of the Black Thursday crash of the Exchange on 24 October 1929 and the subsequent sell-off panic which started on Black Tuesday, 29 October, precipitating the worldwide Great Depression of the early 1930s. The present Exchange building opened in 1903, recognized from the first as an example of masterful architecture, with the six massive Corinthian columns across its Broad Street facade imparting a feeling of substance and stability and, to many, seeming the very embodiment of America’s growth and prosperity. The building has been closed to the public since 9/11.

Nature preserve on the South Shore with hiking trails and shoreline access. Fishing is permitted along the beach or the freshwater pond inside the area. Most of the land is minimally developed, and is an excellent place to observe wildlife. An abandoned orphanage on-site, after which the area was named, burnt down in 2000.

None of Central Park is actual virgin forest, but this is the closest any part of the park gets to feeling like genuine forest. It is beautiful and cool in hot weather. However, like a real forest, it is a mosquito habitat, so make sure to use insect repellent before walking through this part of the park.

A sort of mini forest, described by its designer as a "wild garden," the Ramble is sculpted out of a wooded hillside, with winding paths, rocky outcrops, secluded glades, and a tumbling stream. If one travels through the ramble when the trees are full, it is easy to lose sight of the city's skyscrapers; it's as if you're no longer in Manhattan. The Ramble is also an excellent place to bird watch, with over 250 species of birds that stop here on their migration.

Supported by the Museum of Modern Art, this innovative (and cheap) contemporary art museum is in a former public school building. The conversion left most of the original features of the school - the large ex-classrooms are perfect for installations - and the bathrooms are a blast from the past. P.S.1 is a few blocks south on Jackson Avenue from the Citibank tower; the entrance is a concrete slab (how fitting) which occludes view of the school itself. P.S.1 also has a nice cafe and outdoor seats.

A children's museum home to exhibits featuring Adventures with Dora & Diego.

Kingsland Homestead is a historic home, built by Charles Doughty around 1774. It is now a museum with exhibits about the Victorian era, the slavery in Queens, and how Queens was affected by World War II.

This pretty building was built as Brooklyn's city hall in 1851 and is still a very significant official building in very active use.

Inwood Hill Park contains the last tracts of virgin forest in Manhattan. Many arrowheads and other artifacts of the former Native American occupants of Manhattan Island have been found in this park.

Containing artifacts spanning 4,000 years of art and Jewish culture, with a collection of 26,000 objects – paintings, sculpture, works on paper, photographs, archaeological artifacts, ceremonial objects and broadcast media. The museum also hosts the annual SummerNights concert series and the annual New York Jewish Film Festival.

American woman Jacques Marchais had a dream of traveling to Tibet. While she never made it, her extensive collection of Tibetan artifacts was made into a museum in 1947. The museum now holds over 120 pieces of beautiful Tibetan art. The museum's authenticity was praised by the Dalai Lama.

Built as a pavilion for the 1964 World's Fair, this science center is now full of hands-on exhibits for the public. Highlights include Sports Challenge, Rocket Park (featuring full sized Atlas and Titan tickets), and a science playground.

From its intersection with Park Row (just east of City Hall) you can walk (takes about 20-30 minutes each way), bike, or drive across the historic and iconic bridge to Brooklyn. The view from the bridge is quite lovely, with excellent views of Lower Manhattan and Downtown Brooklyn and good views of Midtown and the New York Harbor in the distance.

This 11 acre lake is one of Central Park's finest spots; surrounded by flowering trees and inhabited by several fish and turtle species.

This pretty 17-story Beaux Arts building was completed in 1904 and designed to be New York City's first air conditioned hotel. It was a residential hotel, and housed a number of very famous people, including the Hall of Fame baseball player, Babe Ruth; the Italian tenor, Enrico Caruso; the modernist composer, Igor Stravinsky; the Italian conductor of the NBC Symphony, Arturo Toscanini; and writers Theodore Dreiser and Isaac Bashevis Singer. The building is now a condominium.

A branch of the Smithsonian Institution, the Cooper Hewitt is devoted to over 240 years of contemporary and historic design, with changing exhibits.