Tokyo, but only four days

You could spend the whole trip in Tokyo and not run out, which is exactly why you should cap it. Four days is enough to feel the size of it — a morning in a quiet shrine, an afternoon lost in a neighbourhood you cannot pronounce, one very good and very small dinner you book in advance.

Base yourself somewhere with a train line that goes everywhere — Shinjuku or Tokyo Station — and resist the urge to see all of it.

Kyoto, with the day trips

Kyoto rewards early starts and punishes mid-morning crowds, so do the famous temples at opening and spend the heat of the day on a long lunch. Use it as a base, too: Nara and its bowing deer are forty minutes away, and Osaka is close enough to go just for dinner.

Three or four nights, not two — the city unfolds slowly, and that is the point.

The third place

This is the one that turns a good trip into your trip. Kanazawa for gardens and gold leaf and almost no foreign tourists. Naoshima if you want an island of art museums and not much else. Koyasan to sleep in a temple and wake up to monks chanting.

Pick one. Add it between Tokyo and Kyoto so the bullet train does the work, and let it be the part you talk about when you get home.