New York is the city that every other city gets compared to, and it has been earning that since long before skyscrapers. Dutch traders built a wall across the bottom of Manhattan in the 1650s, and the street that followed it is still called Wall Street. Roughly 12 million immigrants were processed on Ellis Island between 1892 and 1954, and their children and grandchildren filled the tenements, delis, theaters and jazz clubs you can still visit.
The city is not tidy and it doesn't pretend to be. Subway cars rattle, sidewalks are crowded, and the best meal of the day might come on a paper plate. But it rewards a plan. The distances are bigger than they look on a map, and the five boroughs are really a dozen different cities stacked on one another. Five days lets you see the famous things without turning the trip into a checklist, and still leaves a few hours to sit in a park and watch.
This plan keeps each day to one part of town. Day one is Lower Manhattan with the Statue of Liberty and Ellis Island, day two is Midtown, day three crosses Central Park from the Natural History Museum to the Met, day four is Brooklyn, and day five goes uptown to Harlem and back down to the Village for jazz. We recommend starting on a Wednesday: the Met, the biggest museum, is closed that day, the 9/11 Museum is closed Tuesdays, and this order puts the Met on a Friday, when it stays open until 9pm, and Brooklyn on a Saturday. New York is also the easiest way into the United States as a whole, and the first stop for many longer trips.