New YorkNew York City

Before Europeans arrived, the island of Manhattan and the harbour were part of Lenapehoken, the homeland of the Lenape, who fished, farmed and traded here. Broadway follows an old Lenape trail up the length of the island. In 1624 the Dutch West India Company founded a trading post called New Amsterdam on the southern tip, and in 1626 its director-general bought the island from local people for goods valued at 60 guilders, a story that is more myth than clean contract. A wall built at the northern edge of the settlement gave its name to Wall Street.

The English took the town in 1664 and renamed it New York after the Duke of York. It grew as a port and a place of many nations, since the Dutch had let in Jews, Quakers, Lutherans and others. During the American Revolution the city was occupied by the British for seven years, and after independence it briefly served as the capital of the United States. George Washington took the oath of office as president at Federal Hall on Wall Street in 1789.

The nineteenth century made New York the country's largest city. The Erie Canal, opened in 1825, tied the harbour to the Great Lakes and the interior. The Commissioners' Plan of 1811 laid out the street grid that still covers Manhattan north of Houston Street. Waves of immigrants, first from Ireland and Germany and later from Italy, Eastern Europe and elsewhere, passed through Castle Garden and then Ellis Island, which processed about twelve million people between 1892 and 1954.

In 1898 the five boroughs, Manhattan, Brooklyn, Queens, the Bronx and Staten Island, were merged into a single city, and the population soared. The subway opened in 1904, and skyscrapers went up in the early twentieth century, including the Empire State Building in 1931. The fiscal crisis of the 1970s brought decline and near bankruptcy, and the city recovered in the 1990s and 2000s.

The attacks of 11 September 2001 destroyed the World Trade Center and killed nearly 3,000 people. The memorial pools and the museum opened on the site in 2011 and 2014, and the surrounding district has since been rebuilt. Today New York has more than eight million residents, more than a third of whom were born abroad, and it remains a starting point for millions of newcomers and visitors.

The best single piece of city knowledge is the grid. North of Houston Street, Manhattan is laid out in numbered streets that run east to west and avenues that run north to south, a plan adopted in 1811 that treats the island as rectangles for sale. Fifth Avenue divides east from west, so an address gives you a rough position: East 42nd Street is east of Fifth Avenue on 42nd Street. Downtown, below Houston Street, the old Dutch and English street pattern takes over, and the grid disappears.

Distances follow the grid. Twenty north-south blocks make about a mile, and avenues are farther apart than streets, so walking across town takes longer than walking up or down. That is why the subway matters. It opened in 1904 with a single line and now has about 470 stations and runs 24 hours a day, a feature almost no other big city offers. The system is not perfect: old signals, weekend track work and heat make trains slow, and many stations still lack lifts, but for most journeys it is faster than a car.

Practical rules make the subway easy. Tap a contactless bank card or phone at the gate with OMNY, the tap-to-pay system, and your fare caps after a certain number of rides in a week. Check whether a train is express or local, and whether it is running normally on the weekend, using the MTA app or Citymapper. Stand back from the platform edge, let people off first, move into the middle of the car and keep your phone in your pocket when the doors close.

Buses fill in the gaps, especially crosstown, and they are step-free. Yellow taxis and ride-hail cars are easier with bags, at night and to airports, though traffic below 60th Street can be slow, and a congestion charge applies for vehicles entering the southern part of Manhattan, which raises fares slightly. Ferries link the waterfront, and the Staten Island Ferry is free and gives a view of the Statue of Liberty.

The rhythm of the city follows from this. Walk short distances, take the subway for long ones, and treat the pavement as a busy road: move at the same pace as the people around you, stay to the right and avoid stopping suddenly in the middle of a crowd. Locals cross against the signal, but a visitor should wait for the walk sign, because turning cars and cyclists are quick.

With the grid and the subway understood, you can plan a day in blocks: a morning in one neighbourhood, a subway ride, then a second neighbourhood after lunch. Too many visitors try to see five sights in five neighbourhoods on one day and spend it underground.

Grand Central Terminal opened in 1913 as a rail hub for the New York Central and other lines, designed with a vast concourse, a vaulted ceiling painted with the constellations, and a system of ramps that move people without stairs. It is also a city rescue story. In 1963 the old Pennsylvania Station was demolished, and the loss of that great building helped spark the preservation movement. When Grand Central itself was threatened in the 1970s, a campaign led in part by Jacqueline Kennedy Onassis took the case to the US Supreme Court, which upheld the city's landmark law in 1978. The station you see today was restored in the 1990s.

The Brooklyn Bridge opened in 1883 and was the longest suspension bridge in the world at the time. It was designed by John Roebling, who died of an injury before construction began, and completed by his son Washington Roebling, who fell ill from working in the caissons under the river, and by Washington's wife, Emily Warren Roebling, who managed much of the project. In 1884 the showman P.T. Barnum led twenty-one elephants across it to prove it was safe. Today the wooden walkway above the traffic is one of the city's best free walks.

The Statue of Liberty, a gift from France, was dedicated in 1886 on Bedloe's Island, and the Ellis Island museum next to it tells the immigration story. The Empire State Building, finished in 1931 during the Great Depression, was the tallest building in the world for about forty years, and its observatory remains a popular view. One World Trade Center, opened in 2014, rises 1,776 feet, a figure chosen for the year of the Declaration of Independence.

The 9/11 Memorial is quieter and heavier. Two reflecting pools sit in the footprints of the twin towers, and the names of the victims are cut into bronze parapets around them. A pear tree that survived the attacks stands nearby, and the museum below tells the story of the day. Keep your voice low, allow time for the security check and, if you visit the museum, book a timed ticket.

Downtown Nassau Street and Wall Street hold older buildings from the colonial and early republic period. Fraunces Tavern, on Pearl Street, dates from the eighteenth century, and George Washington bade farewell to his officers there in 1783. A museum upstairs tells the story. Trinity Church and St Paul's Chapel are nearby, and a walk from City Hall to Battery Park passes most of the early city.

The lesson of these landmarks is that New York keeps what it fights for. Ask about a building's story before you go in, and you will see more.

Central Park is not a piece of wild land. It is a designed landscape, planned in 1858 by Frederick Law Olmsted and Calvert Vaux in a competition entry called the Greensward Plan, and built over the following decades by thousands of workers on a site of rocks, swamps and small farms, including a Black community at Seneca Village that was cleared for it. The park covers 843 acres, about 4 km long and 800 m wide, and its lakes, hills, meadows and woodland are all made. The paths were designed so that carriage roads, bridle paths and footpaths cross without meeting.

Bethesda Terrace is the park's formal heart. Its fountain, topped by the Angel of the Waters, was sculpted by Emma Stebbins and unveiled in 1873, and it is named for a biblical pool of healing. The arcade underneath has an ornate tiled ceiling. From the terrace, the lake and Bow Bridge are a short walk, and the Ramble, a wooded area, is a haven for birdwatchers. Enter at 72nd Street and walk north through the Mall, a wide promenade of elm trees.

The Metropolitan Museum of Art was founded in 1870 and opened on Fifth Avenue in its present location in 1880. It holds more than a million objects across some 5,000 years, from Egyptian temples to American paintings. The Temple of Dendur, a gift from Egypt in 1965, is installed in a glass hall beside the park. The European paintings, the American Wing, the Egyptian galleries and the arms and armor are highlights, and the Cloisters, in northern Manhattan, is a separate site for medieval art.

A visit to the Met is a lesson in choosing. The building is too large to see in one day, and a visitor who tries will finish tired and disappointed. Pick two wings, use the museum map, and stop when your attention flags. Buy tickets online, check the weekly closing day, and store your bag at the coat check.

Other museums fill out a plan. The Museum of Modern Art in Midtown, the American Museum of Natural History on the Upper West Side, the Guggenheim on Museum Mile and the Frick, the Whitney and the Museum of the City of New York offer different themes. Check each one's closing day: several close on Monday or Tuesday, and the Met has closed on a weekday for many years.

Parks are the city's living rooms. Washington Square Park, the High Line, Brooklyn Bridge Park and Bryant Park behind the Public Library each have their own crowd and character. Take a picnic from a deli, sit on a bench and watch people, as locals do.

New York food is the food of its arrivals. Jewish immigrants from Eastern Europe brought bagels, lox, pastrami and pickles, all of which became deli staples. Italians brought pizza: Lombardi's on Spring Street is credited as the first licensed pizzeria in the US, opening in 1905, and the thin, foldable slice sold across the city is a New York version. Chinese, Puerto Rican, Dominican, Greek, Korean, West African and South Asian communities have made neighbourhoods into food districts.

For a visitor the simplest meals are the best. A slice at a shop such as Joe's on Carmine Street costs a few dollars, comes hot from the oven, and is eaten standing or on the street. A bagel with cream cheese, or with lox, tomato and onion, is the classic breakfast, and shops such as Ess-a-Bagel roll and boil their bagels by hand. A halal cart chicken over rice from a street corner is the city's cheapest full meal.

For a sit-down meal, the classic New York restaurant is an institution with history. Grand Central Oyster Bar has served oysters and pan roasts in its vaulted room since 1913. Fraunces Tavern serves pub food in an eighteenth-century building. Corner Bistro in the West Village has sold a thick, plain burger with a beer since 1961. These places cost more than a slice but less than the fashionable restaurants, and they give a sense of the city's past.

Prices and manners are the practical side. Menu prices do not include sales tax, about 8.9%, or a tip, which is expected: 18 to 22% at a sit-down restaurant, a dollar or two a drink at a bar, and 15 to 20% for delivery and taxis. Some restaurants add a service charge for large groups, so read the bill. Many small places take cash only, and most bars ask for ID.

Dietary needs are easy to meet in many parts of the city but harder at slice shops and old-style delis. Vegetarian, vegan, halal and kosher options are found throughout, and menus list allergens. Ask for a small change and most kitchens will oblige.

Eat by neighbourhood: the Village for pizza and burgers, Chinatown for dumplings, the Lower East Side for pastrami and bagels, Astoria and Jackson Heights in Queens for Greek and South Asian food, and Harlem for soul food. One meal in each is a good way to see the city.

New York rewards planning that leaves room. The city is dense, the sights are many and the temptation is to see too much. A good three-day plan uses one area per half day, keeps one big timed ticket a day and leaves the evening free. Book the Statue of Liberty ferry, the 9/11 Museum, an observation deck and any Broadway show a week ahead in busy months, and buy from the official sellers only.

Money works in a few habits. Cards and phones are accepted almost everywhere, and the fare on the subway is a tap. Prices in shops and restaurants exclude sales tax, and hotel rates exclude taxes and fees of about 15 to 20%. Carry a small amount of cash for tips, carts and delis. Tips are not optional, and a fair tip is one of the ways the city's service workers are paid.

Manners are brisk, not rude. People walk fast and hold the door for the next person, and a quick 'excuse me' clears the way. Do not stop in the middle of the pavement or the subway stairs, do not block escalators and let people off the train before you board. Do not photograph people at close range without asking, and do not pose with costumed characters in Times Square unless you agree a tip first.

Safety is mostly common sense. Keep phones and bags zipped on crowded trains and near Times Square, be careful crossing the road, and stay to main streets at night. Some subway stations are quiet late at night, so wait near the conductor's car. Check your government's advice for the United States, buy travel insurance with strong medical cover, and know that emergency calls are 911.

Weather shapes the day. Summer is hot and humid, and the subway is even hotter, so plan outdoor sights for the morning and museums for midday. Winter is cold and short-lit. Spring and autumn are the best walking months. A compact umbrella and comfortable shoes are the two most useful items in the bag.

With those habits, three days is enough to see a good sample: a park and a museum, a memorial and a bridge, a station and a slice. Leave the rest for another trip, and end the last day with the bags already in the car.