Three days in New York means running. Five days means you can walk. That extra pair of days is the difference between ticking off a list and getting some sense of what the place is actually like, and the way to spend them is not to add two more landmarks — it is to leave Manhattan.
This plan assumes you want the famous things, because on a first trip you do and there is no shame in it. It puts them in the first half and uses the second half for the city that New Yorkers actually live in.
Day one: Midtown
Start where your hotel probably is.
Grand Central Terminal early, the Chrysler Building lobby, the New York Public Library and Bryant Park, then up Fifth to Rockefeller Center and St Patrick’s.
MoMA in the afternoon. Top of the Rock booked an hour before sunset. Dinner in Hell’s Kitchen, a walk through Times Square after dark, and a Broadway show if you have booked one.
Day two: Downtown
Cross the Brooklyn Bridge from the Brooklyn side at seven-thirty in the morning, having spent half an hour first in DUMBO and Brooklyn Bridge Park.
9/11 Memorial and Museum, the Oculus, then Wall Street, Trinity Church and The Battery.
Evening in Chinatown and the Lower East Side.
Day three: the harbour and the west side
Morning. The Statue of Liberty and Ellis Island ferry, first sailing. Give Ellis two hours; it is the better half and almost everyone shortchanges it. If you want to go up into the pedestal you need to have booked months ago; grounds-only is fine.
Afternoon. Back at Battery Park by about two. Take the subway to 14th Street and walk the High Line from the Gansevoort Street end northward, stopping at Chelsea Market, and finishing at Hudson Yards.
If you would rather have art than a walk, the Whitney is at the southern end of the High Line and is free if you are 25 or under.
Evening. Greenwich Village: dinner on one of the bent streets, then jazz. The Village Vanguard is the one, and it books out.
Day four: uptown
Morning. The Met, two departments only. Or, if you would rather have something smaller, the Frick at 70th Street is an hour and a half and is arguably the better experience — Old Masters hung in a house rather than a gallery.
Midday. Cross Central Park properly, west from behind the Met: the Ramble, Bow Bridge, Bethesda Terrace, then north to the Reservoir if you have the legs.
Afternoon. North to Harlem. Walk Strivers’ Row, which is the best row-house architecture in Manhattan and almost entirely unvisited. The Schomburg Center is free and its exhibitions are serious. If it is a Wednesday, Amateur Night at the Apollo is the best-value evening in New York.
Eat in Harlem — Sylvia’s, Amy Ruth’s or Melba’s — rather than going back downtown.
Day five: Brooklyn and Queens
This is the day that justifies the trip length.
Morning. Prospect Park, which Olmsted and Vaux considered better than Central Park and which most New Yorkers who have walked both agree with. The Long Meadow is a mile of unbroken grass with no building visible from the middle of it. The Brooklyn Museum and Botanic Garden are on its eastern edge; the Saturday farmers’ market at Grand Army Plaza is one of the best in the city.
Walk or take the bus to Green-Wood Cemetery, which was the second most visited attraction in America in the 1860s and is free, enormous and beautiful, with a colony of wild green parakeets living in the gate.
Afternoon. Williamsburg on the L train or, better, the ferry. Domino Park for the skyline, Bedford Avenue for the shops, and Smorgasburg on a Saturday if the season is right.
Alternatively, swap Brooklyn for Queens: the 7 train to Flushing for the best Chinese food in New York by a wide margin, or to Jackson Heights for South Asian and Latin American food on the same block, plus the Museum of the Moving Image and MoMA PS1 in Astoria and Long Island City.
Evening. Ferry back across the East River at dusk. It costs a standard fare and gives you the whole skyline from the water.
Things worth swapping in
If it rains for a day, the museums absorb it — the Natural History Museum, the Tenement Museum and the Intrepid are all indoors and all substantial.
If it is baseball season, a Yankees or Mets game on a weekday evening costs less than a cinema ticket in Midtown and is three hours of watching New Yorkers be themselves.
If it is summer, Coney Island is forty minutes on the D train and the beach is free.
Practical
Five days is roughly fifty miles of walking if you do it this way. Take shoes seriously.
Buy nothing in advance except the observation deck, any show, the 9/11 Museum, the Statue of Liberty ferry and anything at the Vanguard. Everything else is better decided on the day, on the weather.