Almost everything New York eats arrived with somebody. The city’s signature dishes are immigrant food that stayed long enough to become local, and most of them were cheap working food before they were anything else. That is still the best way to eat here: the food that is properly New York is rarely expensive and almost never in a restaurant with a tasting menu.

Here is what to actually eat, and what each thing is.

Pizza, by the slice

Thin, wide, foldable, sold by the slice from a counter, eaten standing up or walking. The New York slice is a specific thing and it is defined by scale — the pies are enormous, so a slice is a meal.

It is descended from Neapolitan pizza brought by southern Italian immigrants around 1900, and the story that New York’s water makes the crust is repeated so often that it has become part of the identity, whether or not the chemistry holds up.

How to eat it: fold it lengthways and eat from the point. This is not affectation; an unfolded New York slice collapses.

Where: any corner shop with a hot counter and a queue of people who are clearly not tourists. Joe’s in Greenwich Village, Prince Street Pizza in Nolita for the square Sicilian, and about four hundred neighbourhood places that are just as good.

Dollar slice shops still exist though the price has moved past a dollar. It is fuel, not dinner.

A bagel, with lox and a schmear

Boiled then baked, dense and chewy, and completely different from the soft supermarket ring. Brought by Eastern European Jewish immigrants to the Lower East Side in the nineteenth century.

The order: an everything bagel with cream cheese — a schmear — and lox, which is cured salmon, with tomato, red onion and capers. Ask for it toasted only if you are prepared for a mild opinion from the counter; a fresh bagel is not supposed to need it.

Where: Russ & Daughters on Houston Street has been an appetizing shop since 1914 and is the reference point. Ess-a-Bagel, Absolute Bagels and a dozen neighbourhood places do it as well and faster.

Pastrami on rye

Beef brisket, brined, rubbed with spice, smoked and then steamed, hand-cut, piled on rye with mustard. A Romanian Jewish preservation technique that became the defining New York sandwich.

Where: Katz’s Delicatessen on Houston, since 1888, and the system is part of the experience — take a ticket at the door, order at the counter from a carver, tip the carver, pay on the way out, and do not lose the ticket. It is expensive and it is enough for two people.

Mustard only. Asking for mayonnaise is a joke people make about tourists.

The halal cart platter

Chicken or lamb over yellow rice with salad, white sauce and, if you are brave, red sauce. Sold from carts on Midtown street corners from lunchtime until very late.

It came out of the 1990s, when Egyptian and Bangladeshi vendors started serving halal food to taxi drivers, and it is now the default late-night meal for a large part of the city. The cart at 53rd and Sixth has a queue at two in the morning.

Cheap, enormous, and better than it has any right to be.

The New York hot dog

Boiled or griddled, in a soft bun, with mustard and sauerkraut or onion sauce. The street cart version is fine rather than good. Nathan’s at Coney Island has been doing it since 1916 and is the original. Gray’s Papaya on the Upper West Side does the classic recession special.

Dim sum and everything in Chinatown

Chinatown covers several regional cuisines that have nothing to do with each other. Cantonese roast meats hanging in the window on Mott Street. Hand-pulled noodles near Eldridge. Fujianese around East Broadway. Vietnamese on Baxter, a legacy of ethnic Chinese who left Vietnam after 1975.

Dim sum in the big banquet halls with carts, before noon at the weekend, is one of the best-value meals in Manhattan.

For the best Chinese food in New York, take the 7 train to Flushing in Queens, which is bigger, newer and covers far more of China.

A soft cake-like disc, half vanilla fondant, half chocolate. It is a cookie in name only. Jewish bakery origin, sold everywhere, and a genuine New York object.

The egg cream

No egg, no cream. Milk, seltzer and chocolate syrup — specifically Fox’s U-Bet — stirred so it foams. A Brooklyn soda fountain drink from the early twentieth century, and one of the few things you can still get for a couple of dollars. Try it at a surviving lunch counter or at Katz’s.

A knish

A pastry pocket of mashed potato, baked or fried. Yonah Schimmel’s on Houston has been making them since 1910 in the same shop.

Cheesecake

New York cheesecake is dense and made with cream cheese, which is what distinguishes it. Junior’s in Brooklyn is the institution.

The things that are not really New York

“New York style” anything outside New York is usually an invention. Cronuts and rainbow bagels are marketing. Deep dish is Chicago and saying otherwise in a bar here is a way to start a conversation you did not want.

How to eat well cheaply

Eat in the immigrant neighbourhoods. Jackson Heights in Queens has South Asian, Tibetan, Colombian and Mexican food on the same block. Sunset Park in Brooklyn has Chinese and Mexican. Astoria has Greek and Egyptian. All of it is a fraction of Manhattan prices and most of it is better.

And eat lunch as your main meal — the same restaurants that charge sixty dollars a head at dinner often do set lunches for twenty.