Nobody arrives in Paris for the first time.

You have been here before — in films, in photographs, in the pages of novels, in the background of other people's holiday stories. Paris is the most imagined city on earth, which means that when you finally stand in it, something strange and wonderful happens. The real city and the imagined one overlap, and for a moment you cannot tell which version you are standing in. Then a taxi honks, a waiter ignores you with magnificent indifference, and the smell of coffee and warm bread drifts from a boulangerie you cannot see yet — and you understand that Paris is even better than the one you invented.

It has had a long time to practice.

The city announces itself best from the water.

A Seine river cruise at dusk is one of those experiences that sounds touristy until you are actually on the boat, watching the light go amber on the stone bridges and the façades of the Musée d'Orsay and the Conciergerie sliding past like pages of a history book nobody asked you to read but you cannot put down. The Eiffel Tower appears at the bend in the river — enormous, iron, improbable — and when it catches the last of the sun it turns a deep rust gold that no photograph has ever quite captured accurately.

At night the tower sparkles. Every hour, on the hour, fifty thousand bulbs light up in a sequence that lasts five minutes and has been making grown adults gasp since 1985. You know it is coming. You watch for it anyway. And when it starts, the people around you — strangers from a dozen countries — all make the same small sound of delight at exactly the same moment, and you remember that this is also what travel is for.

The Louvre deserves more than a day and most people give it three hours, which means they leave exhausted and having seen perhaps two percent of what is inside. The trick is not to see everything — that is impossible — but to choose one wing and give it your full attention.

The Denon Wing holds the Italian masters, and at its far end, in a room that is always crowded and always worth the crowd, hangs the Mona Lisa. She is smaller than expected, behind bulletproof glass, surrounded by the clicking of cameras held by people who are photographing her rather than looking at her. Look at her instead. The sfumato technique — that smoky, borderless blending of shadow and light — means her expression shifts depending on where you focus. Look at her mouth and she seems to be suppressing a smile. Look at her eyes and the smile disappears. Leonardo spent four years on this painting and hid things in it that art historians are still arguing about. You are allowed to take your time.

The walk along the Tuileries Garden afterward — the long gravel promenade between the Louvre and the Place de la Concorde, lined with clipped chestnut trees and metal chairs that Parisians arrange at angles to catch the sun — is one of the great urban walks in the world. Children sail wooden boats on the round pond. Old men play pétanque. A woman reads on a green chair with her shoes off. The city is, in this moment, doing exactly what it has always done.

Montmartre sits above the city like a village that got lost on its way to Provence and decided to stay. The white dome of Sacré-Cœur rises above the rooftops of the 18th arrondissement, visible from most of Paris, a landmark so familiar it has become almost abstract — until you climb the steps to stand beneath it and look back at the city spreading out below you in every direction, grey and gold and vast.

The neighbourhood around it is dense with history. Picasso, Modigliani, Toulouse-Lautrec, and Van Gogh all lived within a few streets of each other here at the turn of the 20th century. The Bateau-Lavoir, the ramshackle building where Picasso painted Les Demoiselles d'Avignon and effectively invented modern art, still stands on Place Émile-Goudeau. The building is unremarkable. The address is not.

The Place du Tertre, the square at Montmartre's summit, is full of portrait artists and tourists buying portraits of themselves — which is exactly as it should be. Duck one street over and the square's noise disappears entirely. You find a café with four tables and a chalkboard menu and a proprietor who seems surprised and mildly pleased to see you, and you order a carafe of house red and a croque monsieur, and the afternoon becomes the kind of afternoon you try to describe later and cannot quite.

Paris feeds you constantly and without apology.

Breakfast is a croissant from a proper boulangerie — laminated, buttery, shattering into flakes with the first bite — eaten standing at the zinc bar of a café with a small, fierce espresso. Lunch is wherever you happen to be: a jambon-beurre from a sandwich counter on a side street, or a bowl of soupe à l'oignon in a bistro with paper tablecloths and a television showing football.

Dinner is the meal Paris takes seriously. The city has more restaurants per capita than almost anywhere on earth, ranging from the grand — marble floors, white-jacketed waiters, menus in the kind of French that requires a dictionary — to the neighbourhood bistro where the same families have been eating the same dishes on the same night of the week for thirty years. Both are worth experiencing. The bistro will cost less and the memory will last longer.

The Marais district is the best neighbourhood for food exploration — a dense, beautiful maze of medieval streets in the 3rd and 4th arrondissements that managed to survive Haussmann's 19th-century reconstruction of Paris and still feels, in places, like the city of five hundred years ago. Jewish bakeries sell rugelach and babka alongside French patisseries selling tarte tatin and mille-feuille. Falafel shops that have been there since the 1970s still have queues at lunchtime. The Place des Vosges, the oldest planned square in Paris, built in 1612, sits at the Marais's heart — its red brick arcades sheltering galleries, cafés, and the house where Victor Hugo lived and wrote for sixteen years.

On the last morning, before the taxi to the airport, there is always time for one more coffee.

You sit at a pavement table in whatever neighbourhood you happen to be staying in. The city is waking up around you — the boulanger arranging baguettes in the window, the school children in their backpacks, the delivery man arguing cheerfully with a parking attendant, the pigeons investigating a croissant someone dropped. Paris, going about its business, entirely unconcerned with your departure.

You will come back. Everyone does. The city has a way of leaving something unfinished in you — a street you meant to walk down, a museum you ran out of time for, a restaurant someone recommended that you never made it to. Paris is inexhaustible. That is, in the end, the whole point of it.