Land at Narita or Haneda. Take the Narita Express (N'EX) or Keikyu Line directly to central Tokyo — the trains are punctual to the minute. Check into your hotel in Shinjuku, the city's chaotic, electric heart.

Even with jet lag, force yourself out in the evening. Kabukicho — Tokyo's entertainment district — is extraordinary after dark: walls of neon, smoke from yakitori grills, the shouted welcome calls of izakaya staff. Stop at the Omoide Yokocho (Memory Lane) for a tiny smoke-filled bar stool and grilled chicken skewers in a lantern-lit alley that has barely changed since 1950. Cap the night at the Tokyo Metropolitan Government Building observation deck — free entry, magnificent night views of the skyline.

Start early at Senso-ji Temple in Asakusa — Tokyo's oldest temple and one of Japan's most visited. Arrive before 8am to experience it in morning mist before the crowds arrive. Walk the Nakamise shopping street for traditional snacks: ningyo-yaki (small sponge cakes), ningyo (doll cookies), and freshly made senbei rice crackers.

Afternoon in Harajuku: walk Takeshita Street for Tokyo's wildest street fashion — fairy kei, decora, and colour-explosion styles you will see nowhere else on earth. Then the adjacent Omotesando boulevard offers a completely different proposition: tree-lined, architecturally extraordinary, with flagship stores by Prada, Dior, and Tod's housed in buildings designed by Tadao Ando and Herzog & de Meuron.

End at the Shibuya Crossing at peak evening hours — stand above it at the Shibuya Sky observation deck or the Starbucks on the corner and watch 3,000 people cross simultaneously from every direction. It is, genuinely, one of the most spectacular urban sights in the world.

Morning at Teamlab Planets in Toyosu (or Borderless in Odaiba if it has reopened by your visit) — an immersive digital art museum unlike anything in the world. Visitors wade barefoot through a room of knee-deep reflective water as infinite flowers bloom and dissolve around them. Book timed-entry tickets weeks in advance; this experience sells out constantly.

Afternoon in Akihabara — Tokyo's legendary electronics and anime district. Even if you have no interest in manga, the architecture of the place is extraordinary: 12-storey buildings wrapped in advertising screens, crane game arcades, maid cafés, and entire floors dedicated to single categories of collector figurines. Multi-floor electronics at Yodobashi Camera; retro game cartridges at Super Potato.

Two hours from Tokyo on the Tobu Nikko Line, Nikko is arguably Japan's most extravagant shrine complex — the mausoleum of Tokugawa Ieyasu, the shogun who unified Japan, built in 1617 and encrusted with 2.4 million sheets of gold leaf. The Tosho-gu Shrine complex features the famous "see no evil, hear no evil, speak no evil" monkeys and the Sleeping Cat carving over one of Japan's most important gateways.

After the shrine complex, take a bus to Kegon Falls — a 97-metre waterfall plunging into a jade-green lake in a cedar-lined gorge. In autumn, the surrounding forest turns a spectacular red and gold. Return to Tokyo by evening.

Take an early Shinkansen from Tokyo Station — the 2 hour 15 minute journey to Kyoto is itself an experience. On a clear day, Mount Fuji appears in a brief window between tunnels, rising enormous and perfectly conical above the Suruga Bay. Book seat 14–16 on the right side of the train (travelling Tokyo to Osaka) for the best views.

Check into your accommodation — if budget allows, a night in a traditional ryokan (Japanese inn) in the Higashiyama district is one of the great travel experiences: tatami floors, futon beds, yukata robes, a private onsen, and a multi-course kaiseki dinner served in your room. Then head straight to Fushimi Inari Taisha as the light drops — thousands of vermilion torii gates climbing Mount Inari for 4km. The lower section is always crowded; walk 40 minutes up and the crowds thin entirely to just you, the pine forest, and fox statues.

Evening in Gion — Kyoto's historic geisha district. Walk Hanamikoji Street at dusk and you have a real chance of spotting a geiko (Kyoto's term for geisha) or maiko (apprentice) in full kimono making their evening rounds between engagements. Do not photograph them without permission — it is genuinely disrespectful, not simply rude.

Start at Arashiyama Bamboo Grove at 6:30am — it is the single most-photographed spot in Kyoto, and between 7am and 10am you will have almost no competitors for the perfect shot. The sound of the bamboo in the wind is as memorable as the sight. Walk through to Tenryu-ji, a Zen temple with a garden designed in 1339 that frames the mountain behind it so perfectly it looks painted.

Cross the Togetsukyo Bridge over the Hozu River and take a rented bicycle into the quieter backstreets of Sagano — passing rice fields, thatched farmhouses, and small stone Jizo statues. Return central for afternoon at Kinkaku-ji (the Golden Pavilion) — its reflection in the pond beneath is one of those images that lives up to every photograph you have ever seen of it, regardless of how many times you have seen those photographs.

The Philosopher's Path is a 2km stone walk along a cherry-tree-lined canal in northeastern Kyoto, connecting Ginkaku-ji (Silver Pavilion) to Nanzen-ji Temple. In spring it is the finest cherry blossom walk in Japan; in autumn the maples turn the canal red and gold. At either end, wander into the quiet side streets where small ceramics studios and handmade incense shops occupy what look like private homes.

Afternoon at Nishiki Market — a 400-year-old covered market running five blocks through central Kyoto, so narrow two people can barely pass. Stalls sell pickled vegetables in 40 varieties, tofu in shapes and flavours Americans have never seen, grilled skewers of octopus-stuffed quail eggs, and matcha candy in bamboo boxes. Eat your way through it slowly.

Late afternoon: book a tea ceremony experience. Several excellent ones operate in Kyoto including En (offers English-language instruction), Ju-An, and Ippodo. You will learn the precise, meditative ritual of preparing and drinking matcha — a practice that has been unchanged for 400 years, and that reveals why Japan's relationship with simplicity and attention is unlike any other culture's.

45 minutes from Kyoto by train, Nara was Japan's first permanent capital (710–784 AD) and contains eight UNESCO World Heritage properties. But the reason most visitors go is simpler: approximately 1,200 free-roaming sika deer wander the park and surrounding streets, considered sacred messengers of the gods. They have learned to bow to receive deer crackers (shika senbei) sold by vendors throughout the park — a bow that visitors return, and that the deer return again, in an absurd and charming three-way negotiation.

At the centre of the park: Todai-ji Temple, housing Japan's largest bronze Buddha — a 15-metre sitting figure cast in 751 AD, housed in the world's largest wooden building. Stand beneath it and it will recalibrate your sense of scale entirely. Return to Kyoto for a final evening in Gion.

Osaka's people have a different personality from Tokyo's — louder, funnier, more direct, and completely obsessed with food. The Osakan phrase kuidaore — "eat until you drop" — is not a metaphor. This is a city where locals will stop you in the street to recommend their favourite takoyaki stall with the same urgency Americans might use to describe a medical emergency.

Start in Dotonbori — the neon-drenched canal district. The giant mechanical crab of Kani Doraku, the running Glico man billboard, the yakitori smoke and the takoyaki (octopus balls, crispy-outside, molten-inside) from Aizuya or Kukuru. Walk across the Dotonbori bridge and eat your way from stall to stall — kushikatsu (deep-fried skewers), okonomiyaki (savoury pancakes), and Osaka's version of ramen with its distinctly clear, sweeter broth.

Afternoon at Osaka Castle — a 16th-century fortress (reconstructed but magnificent) surrounded by a moat and cherry trees, now housing a museum of the Sengoku period when rival feudal lords battled for control of Japan. The view from the top floor across the modern city is striking.

Final morning at Kuromon Ichiba — Osaka's professional kitchen market, in operation since 1822. 180 stalls sell the freshest seafood, produce, and prepared foods in the city. At 8am the market is alive with wholesale buyers; by 9am it fills with visitors eating fresh uni (sea urchin) on rice, grilled wagyu on sticks, and winter melon pickles out of bamboo barrels. A deeply satisfying final morning in Japan.

Optional morning detour to Shinsekai — a faded 1920s entertainment district that has stayed exactly as it was, with blowfish restaurants, retro pachinko halls, and the retro Tsutenkaku Tower at its centre. A completely different Osaka from the Dotonbori tourist strip — quieter, more local, fascinating.

Osaka Kansai Airport (KIX) is 75 minutes by Haruka Express from Shin-Osaka Station. Build in 3 hours before international departure. One last convenience store onigiri at the airport. Japan's convenience stores are genuinely, inexplicably excellent — the Lawson at the terminal will serve you a better rice ball than most US restaurants serve anything.