Central Park
Between 59th Street and 110th Street
Four visitor's centers with free calendars of events and park maps at Belvedere Castle (mid-park at 70th St), Charles A Dana Discovery Center (110th St near Fifth Ave), North Meadow Recreation Center (mid-park at 97th St), the Dairy (mid-park near 65th St)

In Central Park - Places to See and Things to Do
The Children's District (between 59th Street and 65th Street) includes:

The Dairy
(with valid picture ID, children and adults can borrow equipment at the Dairy and square off at the nearly Chess and Checkers House)
Mid-park near 65th Street

Friedsam Memorial Carousel
(58 hand-carved horses, brought from Coney Island and restored in the late 19th century)
65th Street, west of Center Drive

Wollman Memorial Rink
(the place where New Yorkers ice skate in the winter)
Between 62nd Street and 63rd Street, mid-park

Central Park Wildlife Center
(also known as The Zoo, polar bears and other animals)
Between 63rd Street and 65th Street, off Fifth Ave

Tisch Children's Zoo (a petting zoo)
Between 65th Street and 66th Street

Tavern on the Green (famous restaurant)
Between 66th Street and 67th Street

The Mall (lined with statues of famous authors and artists)
66th Street to 71st Street

The Lake
West side of the park, 72nd Street to 77th Street

Loeb Boathouse (rent a boat to paddle around the Lake)
Mid-park at 75th Street

Strawberry Fields (memorial to John Lennon, directly across from the Dakota Apartments where he was shot)
West of the Lake at 72nd Street and West Drive

Conservatory Water (competitive model-yachters gather to race; rent a remote control sailboat)
74th Street off Fifth Avenue

Alice in Wonderland and Friends and Hans Christian Andersen statues
(the NY Public Library sponsors summer storytelling at the Andersen statue)
74th Street off Fifth Avenue

The Great Lawn
80th Street to 85th Street, mid-park

Belvedere Castle (education and information center and observatory)
Just off the 79th Street transverse

Delacorte Theater (home to Shakespeare in the Park)
80th Street, mid-park

Shakespeare Garden
(said to contain every plant, flower and herb mentioned in the Bard's works)
81st Street, mid-park

Swedish Cottage Marionette Theater
(former 19th century schoolhouse, hosts regular puppet shows)
81st Street, mid-park

Reservoir (jog around the Reservoir for views of the Central Park West skyline)
From 86th Street to 95th Street

Conservatory Garden
(Burnett Fountain in the center of the south section depicts Mary and Dickon from The Secret Garden by Frances Hodgson Burnett)
105th Street near Fifth Avenue

Charles A Dana Discovery Center (conservation exhibitions and activities and tours)
110th St near Fifth Ave

Cooper-Hewitt, National Design Museum
(Smithsonian Institution: displays a virtual cornucopia of decorative and design arts in Andrew Carnegie's Upper East Side mansion)
Two East 91st Street, on 5th Avenue

National Academy Museum and School of Fine Arts
(one of the oldest artist-run organizations in the United States; houses a sizeable collection of American Arts; designated a New York City landmark)
1083 Fifth Avenue at 89th Street

Solomon R. Guggenheim Museum
(Frank Lloyd Wright architected this building, now designated the youngest New York City landmark; works from artists of the 19th and 20th century including: Brancusi, Braque, Calder, Chagall, Robert Delaunay, Giacometti, Kandinsky, Klee, Leger, Miro, Picasso, and Van Gogh)
1071 Fifth Avenue at 89th Street

Metropolitan Museum of Art
(every category of art in every known medium from every part of the world during every epoch of recorded time is represented here)
1000 Fifth Avenue
Fifth Ave at 82nd Street

El Museo del Barrio
(Founded thirty years ago, El Museo del Barrio is New York City's only Latino museum dedicated to Puerto Rican, Caribbean and Latin American art)
1230 Fifth Avenue at 104th Street

The Museum of the City of New York
(established in 1923 to collect, preserve, and present original materials related to the history of New York City)
1220 Fifth Avenue at 103rd Street

Jewish Museum
(a major American art museum, but also the largest Jewish museum in the Western hemisphere)
1109 Fifth Avenue at 92nd Street

Goethe House German Cultural Center
(organizes and supports a wide range of international cultural exchange programs in close cooperation with partners and institutions in both the host countries and in Germany)
1014 Fifth Avenue at 82nd Street

The Frick Collection
(housed in the former residence of steel magnate Henry Clay Frick, and is one of the  preeminent small art museums in the USA, with a very high-quality collection of old master paintings housed in 16 galleries within the former mansion)
1 East 70th Street, at the corner of Fifth Avenue and 70th Street, facing Central Park

The Whitney Museum of American Art
(features one of the most important collections of contemporary American art of the 20th century. Founded by Gertrude Vanderbilt Whitney in 1931 with 700 works of art from her own estate, the museum displays paintings, drawings, prints, sculptures, installations, video and photography)
945 Madison Avenue at 75th Street

Gracie Mansion
(official home of the Mayor of New York City)
East 88th Street

Upper West Side
The Upper West Side, located between 59th Street and 110th street west of Central Park, offers exciting dining, shopping, and cultural activity. Because of the continuous bustle, Broadway above 96th Street feels safe, even at night. However, the side streets that intersect 96th Street, as well as Amsterdam and Columbus Ave above 98th Street should be avoided at night.

Upper West Side - Places to See and Things to Do
American Museum of Natural History (world's largest collection of vertebrae fossils including dinosaurs, ancient fishes and mammals)
Central Park West at 79th Street

Lincoln Center
(16 acre center for performing arts with 11 facilities. including the Metropolitan Opera House, New York State Theater/home of the New York City Ballet, Damrosch Park, Guggenheim Bandshell, Avery Fisher Hall/home to the New York Philharmonic, Vivian Beaumont Theater, Mitzi E Newhouse Theater, the Julliard School, Alice Tully Hall, Walter E Reade Theater)
Columbus Ave between 62nd Street and 66th Street

Dakota Apartments
(site of the filming of Rosemary's baby; John Lennon was assassinated outside
1 West 72nd Street, corner of Central Park West

Morningside Heights
Morningside Heights, between 110th Street and 125th Street and between Amsterdam Avenue and the Hudson River, is centered between the glamour of Upper West Side and Harlem.

Morningside Heights - Places to See and Things to Do
General Grant National Memorial (Grant's Tomb - largest mausoleum of its kind in America - rests atop a hill overlooking the Hudson River)
Near the intersection of Riverside Drive and 122nd Street

Barnard College
116th and 120th Streets along the west side of Broadway

Columbia University
Morningside Drive and Broadway, from 114th Street to 120th Street

Cathedral of St John the Divine
(largest cathedral in the world, under construction since 1892; the central nave contains a 100-million-year-old nautilus fossil; world's second largest organ stop)
Amsterdam Ave between 110th Street and 113th Street

Riverside Church
(inspired by Chartres Cathedral; interdenominational; tower observation deck looms over 360 feet above Riverside Drive with terrific view; concerts on the world's largest carillon with 74 bells, in memory of John D Rockefeller's mother, resonate on Sundays)
490 Riverside Drive at 120th Street

Harlem
Harlem is Manhattan's largest neighborhood. It begins at 110th Street and runs to the 150s, between the Hudson River and the East River. The poor and dangerous Harlem of cinema fame is found mainly in the area south of 125th Street in the Manhattan Valley, particularly along Frederick Douglass and Adam Clayton Powell Boulevard. Avoid this area after dark. Central Harlem's main thoroughfare is 125th Street. Many of the streets in this neighborhood were renamed for past black leaders: Sixth Avenue (Lenox Avenue) is also referred to as Malcolm X Boulevard, and 125th Street is also known as Martin Luther King Boulevard.

Spanish Harlem, known as El Barrio, is between 96th Street and 125th Street on the east side. The main artery of Spanish Harlem is East 116th Street. The anarchic chaos that Spanish Harlem experienced during the late 1980s has calmed, but widespread poverty remains, so avoid this area after dark.

Harlem - Places to See and Things to Do
Jackie Robinson Park (includes a bronze statue of the famous baseball player)
145th Street -152nd Street, between Edgecombe and Bradhurst Ave

Marcus Garvey Park
(named after the advocate of the "Back to Africa" movement)
120th Street - 124th Street between Fifth Avenue and Madison Avenue

City College of New York
(the nation's first public college and alma mater of Woody Allen, Colin Powell, Edward Koch, Jonas Salk, and Walter Mosley)
Convent Avenue from 130th Street to 140th Street

The Schomburg Center for Research in Black Culture
(research branch of the New York Public Library houses the city's archives of black history and culture; also houses the American Negro Theater and The Langston Hughes Auditorium)
515 Lenox/Sixth Avenue at 135th Street

Graffiti Wall of Fame
106th Street and Park Ave

Riverbank State Park
(features ice and roller skating, pool, tennis, tracks, baseball diamonds, and picnic fields)
Along the Hudson River

Striver's Row
(historic 1891 brownstones featured in Spike Lee's Jungle Fever; part of the St. Nicolas Historic District)
138th Street and 139th Street, between Powell and Frederick Douglass Boulevard/Eighth Avenue

Sugar Hill
(birthplace of Sugarhill Records, the rap label that created the Sugarhill Gang; Duke Ellington and W.C. Handy lived in the neighborhood, as did W.E.B. DuBois and Thurgood Marshall)
143rd Street to 155th Street, between St. Nicholas and Edgecombe Avenue

The Apollo Theater
(distinguished and legendary landmark in Harlem; originally opened as a burlesque hall to an all-white audience in 1913, but in the 1930s it became home to legendary jazz greats like Billie Holiday, Ella Fitzgerald and Duke Ellington)
253 West 125th Street, between St. Nicholas Avenue and Frederick Douglass Boulevard