It makes perfect sense that Tokyo is Guardian readers' favourite overseas city. Now that Shanghai looks in parts like Beverly Hills and Delhi is lighting up with Thai restaurants, there are few cities on the planet that are less western than Tokyo – even if it's not necessarily a part of any east that you might recognise. The abiding allure of Japan's huge network of tiny details is that, like something in a Salman Rushdie novel, it seems to blur all notions of high and low, east and west, old and new into one state-of-the-art global amusement park that is wildly fresh and novel in its best incarnations, and at least zany in its worst.
I've lived at a safe distance from Japan's capital for 23 years now, in Kyoto and Nara, three or four hours away by train and several centuries away in terms of their antique pasts. But if I were going to Tokyo tomorrow, I would, on arrival, hold off on the "maid cafes" in the nerds' electronic hive of Akihabara, on the Hysteric Glamour fashions around Harajuku, even on the gleaming shops of the Ginza that have long made Tokyo seem an early visitor from the 23rd century. Instead I'd begin by looking for the old.
The evergreen riddle of Japan, after all, is that all its revolving-door fashions, fascination with the west and hunger for the new never seem to make it any less Japanese at the core; the place is like a froth of shifting surfaces and flashing images projected on an old, strangely shaped piece of wood that never moves. My Japanese wife is mad for Marilyn Manson and Metallica and used to gun her Honda Hurricane around the winding streets of Kyoto. But every day, before she heads out in her leather jacket, she places fresh water in a bowl around the small shrine she's set up, and an apple for the gods; she cleans every item of clothing either of us have used the previous day; and then she puts on a CD of monks chanting and sits stock-still in her chair in meditation.
Much of Japan is like that still, and if you're arriving in Tokyo soon – especially if you're coming from far away and are jet lagged – the first place I'd recommend you see is the Tsukiji fish market (tsukiji-market.or.jp) visiting ideally as close to 5am as possible. Nothing will convince you more quickly that you're not in Kansas (or Hampstead) any more, and the sushi you can try nearby will tell you you're not at Wagamama either.
From there I'd suggest heading to Ueno, a slightly down-at-heel area, built around a park, that still has a faintly rural feel and reminds you of what Tokyo used to be when its Meiji refashioners, in the late 19th century, took their cues from London and Paris. Wander through the Tokyo National Museum (tnm.go.jp/en), which has perhaps the best collection of classical Japanese art in the world.
At dusk, for this opening immersion, I would head towards Asakusa Kannon Temple, whose great front gate makes you feel as if you're entering a Hiroshige woodcut. One of the centres of Shitamachi, the old "Low City" of Edo (even by the end of the 18th century the city was the world's largest in terms of population), it still has echoes of the time when it sat at the heart of a bustling entertainment district, home to the country's first cinema and first music hall.
The power of Japan, for me, lies in everything you find here that you couldn't imagine seeing in another country, even – sometimes especially – when what you think you're enjoying is something foreign, deliciously lost in translation. Last month, McDonald's outlets across the nation were serving Tsukimi, or "Moon-Viewing" burgers – a moon-like fried egg between the buns – in honour of the harvest moon that has been ritually observed for millennia across east Asia.
On your second day, there's something to be said for going to Kamakura (city.kamakura.kanagawa.jp/english), the leafy, temple-filled mini-Kyoto that's only an hour away from Tokyo by train. Just ramble through its leafy lanes, walk into shrines that look deserted, breathe in the quiet of a place that was Japan's capital from 1185 to 1333 and has been a kind of resting place ever after.
It's part of the curiosity of contemporary Japan that it presents you with some of the most jangled and mishmashed, unattractive urban landscapes in the world and yet, in many places, every little shop and cafe you enter will be immaculate and exquisite, whether it plays only Beatles records or Mozart. The details are often perfect, even as the whole sounds like 15 languages shouted all at once. And to savour Japan, it makes most sense to seek out its privacies, its secret corners; until I came here, I never realised that the society famous for its conformist surfaces is – for that very reason, perhaps – a home to wild obsessives, who have collected every King Crimson bootleg in existence or will show you their collection of videos of ancient Hawaii Five-O episodes.
In these ways, it's best to browse Tokyo, to get lost, almost as if you were in some virtual reality; more than any city I know, the place is like a website, alight with odd links, hobbyists' addenda, animated figures and racing graphics. And once you've tasted a little of the old city, like striking a gong or a temple bell before a feast, you can fling yourself into the new. The Mori Art Museum (mori.art.museum/eng) on the 53rd floor of the Mori Tower in the Roppongi Hills complex, say, whose sleek passageways and views over the city and make it look like a high-definition TV screen writ large. There are dog rental stores around town, vending machines selling underwear and whisky, and three-star Michelin restaurants with only a single table and a few seats at the bar (Yukimura, 1-5-5.Azabu-Juban, Minato-ku, +81 3 5772 1610). At the New Otani hotel (newotani.co.jp/en/tokyo) you can enjoy a 400-year-old Japanese garden and a rooftop rose garden with 2,000 bushes, where fireflies flicker in the summer.
The very best side of Tokyo comes out – though perhaps this is true of every place – when you can see the strange and the familiar all at once. Go out drinking in Roppongi on a Saturday night and you'll half-believe you're in LA, or at least Hong Kong, among the Romanian restaurants and Filipina hostess clubs; then, on Sunday morning, walk down Omotesando street, past all the note-perfect French cafes and high-end boutiques, with the Kings Road of Takeshita street just a short hop away.
On Sunday afternoons, on Jingu Bridge, at the end of Omotesando, "cosplay" (a mix of "costume" and "play") girls from the suburbs come out in their wild outfits, dressed as nurses or goths or dominatrices or Alice in Wonderland. Costumes, you will soon register, are as outlandish as uniforms are constant in Japan, if only because the same people who are dressed down for six days every week get their own back by dressing up on Sundays.
Right behind the bridge, wide pathways take you to the Meiji shrine (meijijingu.or.jp/english), where you are back in the thick, textured, slightly elusive place that has altered very little over centuries. Shrine maidens dressed all in white – traditionally they were virgins – are selling good luck charms for passing exams to the wild teenage girls in microskirts and fishnet stockings whose hairstyles seem to have been copied from Lady Gaga.
Everywhere in Japan there are things that are worth doing just because they can't be done in quite the same way anywhere else. Try to arrive at a fancy department store at 10 am, when it opens, to see the scores of perfectly coiffed employees lined up to call out a formal welcome. Try Isetan (isetan.co.jp) in Shinjuku; you can spend the next many hours lost in the capacious food halls in its basement. Look for the three-course "teishoku" set lunches, which will offer you the same food you'd spend £20 on at dinnertime for a third of the price. And never spurn a convenience store, because there is more in their small heaven and earth than is dreamed of in your philosophy.
The first time I came to Japan, as a sightseer 25 years ago, I made sure to take myself to Tokyo Disneyland (tokyodisneyresort.co.jp) so I could see the whole seamless, public and well-organised society in miniature; I could get a (cartoon version, but defiantly partisan) tour of Japanese history in one pavilion, eat melon sorbets in another and see on every side how Japan had taken something deeply American and made it entirely its own (and cleaner, quieter, more efficient). In time though, after I came to live here, I began to see how much of Japan can be enjoyed as a kind of theme park, where most people are dressed up to play a part, as polite, chirpy and eager to please as one of Walt Disney's Mouseketeers, and inhabiting what looks less like real life and more like a super-synthetic version of The Happiest Place on Earth.
There are 35 million people in Greater Tokyo – more than in all of Canada – and when you arrive at Tokyo station you may feel that they're all streaming past you at the same time. Two million souls do indeed pour through Shinjuku station every day. But what ultimately stays with many a visitor to the epicentre of Japan are the moments of stillness, of collectedness, of almost mysterious remoteness, where you see the changeless nerve centre from which all the wild changes arise.
Pico Iyer is the author of nine books, including The Lady and the Monk (IB Tauris), about his first year in Japan
