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The mistake first-timers make is trying to add Hiroshima, Hokkaido and Okinawa to a ten-day trip. Here is the route that leaves you time to actually look at things.
Days 1–4: Tokyo
Land, adjust, and give the city four nights. Split your days between the neon districts and the low-rise neighbourhoods.
Days 5–6: Hakone
One night in an onsen ryokan, with a lake view of Fuji if the weather cooperates.
Days 7–9: Kyoto
Early starts for the shrines, afternoons in the craft districts.
Day 10: Osaka
Eat, then fly home from Kansai rather than backtracking to Tokyo.