
Himeji exists on most itineraries for one reason — Himeji Castle, widely considered the most beautiful surviving castle in Japan and one of the few that escaped both fire and bombing. It's an easy half-day stop on the Shinkansen line between Osaka and Hiroshima.
You can do Himeji as a 3-hour stop on a Shinkansen ticket between Osaka and Hiroshima — leave bags in a station coin locker and pick them up on the way back.

Fukuoka
Kyushu's friendly capital and home of Hakata ramen

Hiroshima
Peace Memorial city and gateway to Miyajima

Osaka
Japan's loudest, hungriest, most fun city

Kyoto
Temples, geisha districts, and a thousand years of capital

Kanazawa
Samurai history, geisha streets, and one of Japan's great gardens

Shirakawa-go
UNESCO mountain village of thatched gassho-zukuri farmhouses

Mt Fuji
Japan's iconic peak and the lakes and shrines around it

Tokyo
The most relentless, addictive, and well-fed megacity on earth