There’s never enough time to explore New York City . That said, you can also see a lot in a few days, as Manhattan , where most of the city’s most famous attractions are located, is a compact place with an excellent public transportation system, not to mention being the best place in the world to stroll.
On your third day, explore the streets of Chinatown , SoHo , and Greenwich Village . At night, take in a Broadway play , visit a jazz club , pop into one of Lower Manhattan’s speakeasies , and eat in one of the city’s many ethnic restaurants.
If you have more time, spend a day at the Museum of Modern Art  and take a stroll down 5th Avenue  and across East 42nd Street, visiting Rockefeller Center , St. Patrick’s Cathedral , the New York Public Library  and Grand Central Station  along the way. Or, explore the American Museum of Natural History  and take the A Train up to revitalized 125th Street in Harlem .
A fifth day could be spent shopping, visiting another museum, and taking a closer look at Central Park. On your sixth day, walk over the Brooklyn Bridge  to Brooklyn Heights  or take a day trip to Coney Island .