MY first glimpse of Tokyo is under a sharp blue winter sky. The city curves around an enormous bay and sprawls as far as the eye can see, the mythical cone of Mt Fuji standing watch in the distance, snow-capped and splendid, like Hokusai and cherry blossom were created for it.

As we drive over the Rainbow Bridge, Tokyo shines in the sun, all white concrete apartment buildings and vertical pillars of glass and steel. This neat, futuristic-looking metropolis gives little hint of its personality, but to my jet-lagged sensibilities it feels like some brave new world that is both serene and exciting, at once familiar while unmistakably different.

Down at street level, you realise Tokyo is almost all new. There seems so little that is more than 70 years old – the city’s main station, some temples and a couple of Art Deco department stores feels about it. Before they obliterated Hiroshima and Nagasaki in 1945, the Americans bombed Tokyo almost out of existence; more than 100,000 people died. What stands there now is very Bladerunner-ish: elevated railways, four-lane arterial roads, raised glassed-in walkways, subterranean passages, vertiginous escalators and paved piazzas.

Then you start to get a sense of Tokyo’s jam – vivid splashes of billboard colour; a swathe of evergreen park; the Day-Glo fashion tribes; a golden ‘head of beer’ sculpture on top of Asahi Brewing’s HQ (that most people think resembles a giant sperm); doe-eyed Manga graffiti; a red and white Eiffel Tower confection; and people – thousands of people, swarming the streets like ants. It is exhilarating.

And then as it gets dark, the chameleon city blinks and slips its skin for neon. This dazzling nightly show has come to define Tokyo’s modernist vibe, its neon hoardings splashing pools of light on to the crowded rainy streets. The famous Shibuya crossing feels like the epicentre, a star-shaped convergence of zebra crossings where black-clad pedestrians pour out of the nearby Shibuya station, streaming across from several different directions. There is no better view of it all than from the first-floor window of Starbucks right opposite.

Identical streets of big department stores, designer shops and fast-food chains line up, eventually giving way to the drug stores and the coffee bars, the noodle joints, massage parlours and 100 yen shops (where you will find some of the best and cheapest Japanese souvenirs). And hidden away behind it all, if you know where to look, is Golden Gai. This shady little network of criss-crossing lanes is a hipster’s paradise of tiny little bars (average punter space: seven drinkers) where you can nurse a rather expensive Japanese whisky and hang out with the cool people.

The lights are low, the music is vintage or impossibly current and the people are interesting. Don’t mind the cover/admission charge; if you find a bar without one, they’ll just whack the difference on to your drinks bill. It’s an experience to savour, and who doesn’t want to boast of a night in the drinking dens of downtown Tokyo?

The Hoshinoya Hotel – riding high on Conde Nast Traveller’s “Gold List 2018” – sits opposite the East Gardens of the Imperial Palace where any day now the pink and white cherry blossom will bloom, drawing visitors from all over the world. Hidden within a rather ordinary-looking skyscraper is a traditional-style Japanese inn orryokan. A closer look reveals a building completely veiled by a delicate lattice work of leaf patterns, almost invisible by day but exquisitely illuminated at night when the interiors are lit.

The idea of creating something normally found deep in the Japanese countryside or high up in the mountains, is to bring some of the customs, values and seasonal living to the big city. And it works beautifully, creating a really lovely, peaceful space to escape the crazy-busy outside. Stepping through the huge larch-wood door, we remove our shoes and enter a long tatami-floored hallway. Each floor has its own communal space where guests can read, relax, have breakfast or enjoy beer in the evening.

Rooms are elegantly minimal and spacious and designed in traditional Japanese style – springy tatami rush mats underfoot, sliding shoji paper screens, the subtle scent of sandalwood, and kimonos for lounging around in. But the star attraction is the magnificent outdoor onsen baths (segregated for men and women) where foreign guests can first glimpse the age-old bathing rituals of the Japanese. After showering as you perch on a little wooden stool, you wade naked through the rising steam and take your place under the open sky, 23 floors up, immersed in natural hot spring water that bubbles up 1500 metres beneath Tokyo’s streets.

Beyond the city, any number of bullet trains (which bizarrely, play Auld Lang Syne before the doors close to depart) will speed you east, west and north through a rich and varied landscape that is 70% mountains. Europeans may be surprised to learn that Japan has its own Northern Alps and an extensive range of ski resorts that easily match anything France and Switzerland have to offer. And then there is the magical Japaneseyuki – snow – light, fluffy and perfect for off-piste snow safaris. And there are more than 100 ways to express it in Japanese from ‘peony’ snow (big fat beautiful flakes) to ‘rice-cake’ snow (dense and sticky).

First stop is Hakuba, setting for the 1998 Winter Olympics and considered one of the country’s best ski regions. There are nine resorts stretched across a broad valley, with more terrain, vertical rise and advanced ski and snowboard slopes than anywhere else in Japan. Refreshingly, Happo-one resort lacks the chocolate-box tweeness of its European counterparts to the point of purely functional looks, but the slopes are well groomed. The real beauty is reserved for the mountain tops where spiny ridges are cloaked in trees, and ski runs weave through little forests of deciduous trees, each branch cake-frosted with snow.

After a chilly day on the slopes, returning to the Kai Alps mountain inn, we find a haven for weary skiers. Some rooms have their owntsubo or mini-onsen (fashioned like one half of a giant whisky barrel) and once more we are supplied with the traditional Japanese wear, this time ayakuta wrap gown and a padded overcoat to keep out the cold. The inn, which reopened in December after extensive refurbishment is part Monocle world-traveller fantasy, part authentic Japanese cultural experience, combining modern design with traditional customs such as onsen bathing andkaiseki cuisine, all set against a backdrop of the Northern Alps.

Pride of place is the Shinshu-style irori, a traditional sunken hearth where frozen skiers gather round to warm themselves, while a sweet-faced old man deftly makesoyaki dumplings over an open flame to go with the hot sake. Later as we submerge ourselves in the outdoor onsen, overlooking larch trees and mountains, a flurry of snow starts to fall, creating a memorable snapshot of rural Japan.

Dinner is a 10-course event, a succession of stunning dishes composed for texture, colour and flavour, served in a shoji-screened dining space in the restaurant. Marbled beef, fresh sashimi, simmering hotpots, nose-tickling wasabi, crunchy pickles: it is an eye-opening experience of the Japanese version of haute cuisine.

It’s all a far cry from our next lodgings in the resort of Naeba, this time the rustic Wadagoya mountain hut. Here it’s futons on the floor, a roaring fire, a bar full of international skiers and what looks like a fast-food kitchen which is actually turning excellent hearty fare. It’s a ski-in, ski-out affair, high up on the mountain in Kagura, where we barely meet a soul. These slopes are almost ethereally peaceful, where the only sound is the schiff-schiff of your skis and the overhead whirr of the chairlift. Knee-deep soft powder attracts the adrenaline junkies off piste as they sweep down through the trees. It looks like fun, but it’s only for the technically accomplished. There is as much pleasure to be found gliding down the wide, well-groomed slopes.

A three-hour drive brings us back to Tokyo and the vertiginous Park Hotel with more Bladerunner views over the metropolis. Red aircraft warning lights blink above, a million lives carry on behind the lit apartment windows, and long, snake-headed trains wind sinuously through the city below. Again there is this strong feeling of familiarity and otherness in this city of contrasts: of ancient culture and modernity; of boldness and reserve; youth and age; east and west; smart technology and old-school spirituality. Those contrasts play out in Tokyo’s citizens, where station staff will bow to you as you exit the ticket barriers, while pink-haired teens in polka dots and platforms will look at you with a mixture of curiosity and derision.

Culturally, the Japanese seem to live quite different lives. The dominant religions of Shinto and Buddhism mean they cultivate a more spiritual existence and adhere to ancient customs and values, prizing reverence and respect. But their reputation for being cool and dispassionate does them a disservice – we were constantly met with warmth and kindness. Their unfailing politeness is almost shocking, so lacking is it in our own culture. And where else could you walk down a city street and see bicycles unchained because stealing is virtually unheard of?

Our last jaunt is an early one with a 5am rendezvous at Tsukiji fish market for the day’s tuna auction, a hotly anticipated (free) ticket that is open to just 120 spectators every morning. As it’s first-come-first-served, some people queue from 1am to get a coveted spot, but we turn up on spec just before 5am and are waved through by a very jolly man in uniform.

We are led through the bustling market military style – one false move could see us being mown down by a speeding forklift truck – till we reach the special tuna auction shed where grave-looking men eye the fish, prodding for freshness. The youthful auctioneer turns in an almost operatic performance, singing out each of the bids, raising the stakes and the tension with each call. These big beasts of the sea come frozen, great obelisks of blood-red flesh stacked up on trailers then laid out in rows for the sharp eyes and noses of the buyers. Considered the most important tuna market in the world, Tsukiji is a spectacle worth seeing.

Afterwards we wander down one of the many narrow market lanes, watching young men sharpen huge sword-like knives and old women cook oysters over purple gas rings. It is 6am and we are eating raw fish with fresh wasabi. It could only be Tokyo.

FACT FILE

Getting there

JAL flies daily from Heathrow to Tokyo; economy specials from around £650 return.www.jal.com

Where to stay

Hoshinoyo Tokyo & Hoshino Kai Alpes Superluxe modern incarnation of the traditional Japanese inn. Fine-dining Japanese cuisine and beautiful outdoor onsens. Rooms from around £800 per night.www.hoshinoresorts.com

Park Hotel Tokyo Cool, arty, well-priced, four-star hotel with terrific views across the city from the 25th floor up. The rooms on the 31st floor are decorated by well-known Japanese artists. Check out the waving cat room. Rooms from around £144 per night.

parkhotel-tokyo.com

Prince Hotel, Naeba Ski Resort Huge, sprawling hotel complex at the foot of Naeba’s slopes. Extremely comfortable, great value, with mountain views and lots of dining options. Plus the best apres-ski massage in Japan. From around £58 per person per night. princehotels.com

Wadagoya Mountain Hut, Kagura delightful rustic retreat that is basic but comfortable and deposits you straight on to the mountain top in the morning. Great fun for groups and just £53 per person per night.princehotels.com