Two weeks in Japan

Three days in Tokyo cover the main districts – Asakusa and Ueno, Shibuya and Harajuku, Shinjuku, Ginza and the Imperial Palace. On the fourth day, a trip north to Nikko by Tōbu limited express or by Shinkansen and JR local train leads to the ornate Tōshō-gū shrine, mausoleum of Tokugawa Ieyasu, set among cedar forests, with Lake Chūzenji and the Kegon Falls further up the mountain.

The Hakone loop – mountain railway, cable car, ropeway over Ōwakudani and boat across Lake Ashi – offers volcanic scenery and, in clear weather, views of Mount Fuji. A night in a ryokan with a hot-spring bath breaks up the journey before heading west.

From Odawara, the Shinkansen runs to Nagoya, where the JR Hida limited express climbs through river gorges to Takayama. The old town's Sanmachi Suji streets of dark wooden merchant houses, sake breweries and morning markets reflect its wealth as a castle and craft town of the Hida region.

The next morning, express buses cross the mountains to Shirakawa-go, a village of steep-roofed gasshō-zukuri farmhouses, and continue to Kanazawa. Seats should be booked in advance, and luggage is best sent ahead.

Kanazawa, spared by wartime bombing, preserves samurai and geisha districts, the Kenroku-en garden – one of Japan's three great gardens – and the 21st Century Museum of Contemporary Art. Omichō market is known for seafood from the Sea of Japan.

In the late afternoon, the Hokuriku Shinkansen and a change at Tsuruga to the Thunderbird limited express bring the route to Kyoto.

Three days in Kyoto leave time beyond the highlights: Fushimi Inari, Kiyomizu-dera and Gion; Kinkaku-ji, Ryōan-ji and Arashiyama; and quieter places such as the Philosopher's Path, Daitoku-ji's sub-temples or a tea ceremony. The eleventh day is for Nara, with Tōdai-ji, Nara Park and Kasuga Taisha, possibly combined with Hōryū-ji, home to the world's oldest surviving wooden buildings.

The Sanyō Shinkansen reaches Hiroshima from Kyoto in under two hours. The Peace Memorial Park, the Atomic Bomb Dome and the Peace Memorial Museum are a sobering and essential visit. In the afternoon, a train and the JR ferry lead to Miyajima, whose Itsukushima Shrine stands over the water; staying overnight on the island lets visitors see it after the day crowds leave.

On the way back east, Himeji Castle, the finest surviving original castle in Japan, is a short walk from the Shinkansen station. The evening belongs to Osaka: Dōtonbori, Shinsekai and the street food of Namba. The last day can include Osaka Castle or shopping in Umeda before the train to Kansai Airport.

In winter, when the mountain roads are snowy, the Alps leg can be replaced by Kanazawa alone, reached directly from Tokyo on the Hokuriku Shinkansen, or by a trip to Matsumoto and its black castle. Travellers who prefer the countryside can add the Kumano Kodō pilgrimage trails or a night at a temple on Kōyasan; those drawn to islands can continue from Hiroshima to Shikoku or the art island of Naoshima.