Akane
I will have 1 free day after my tour ends. We will have already spent 2 nights in Hiroshima. We will have seen Tokyo, Yokohama, Kyoto, Osaka, and Hiroshima on the tour. Where should I see in the time that I have? After that I will be leaving Japan from Kansai International Airport.
Is there a city/place that I can go visit that is not too far away and is convenient to get to the airport from?
Akane
If you have 2 nights at Hiroshima, I am sure they will have taken you to see the important sights there. Spend your time at Okayama/Kurashiki and/or Himeji. Buy single tickets between Hiroshima, Okayama, Kurashiki up to Himeji. Once you get to Himeji, get the Kansai Area Pass 1-day version. It will cover your ride from Himeji to KIX airport, including Haruka Express but not the Shinkansen, saving you about 2,000 Yen.
