Originally Posted by joejones

You also want to have enough time in Hiroshima to go out to the shrine on Miyajima, which will take up half a day in itself, and to see the A-bomb museum and eat okonomiyaki. That's stretching the limits of a comfortable day trip, so it might be worth spending the night, and doing Himeji and Osaka on the way there or the way back.

If you're flying home on UA, you could make Nagano your final stop, then take the shinkansen back to Tokyo in the morning and have plenty of time to connect to the Narita Express and make your flight at 5pmish.