Traveling in Japan Nov 1-12. Planning to arrive Tokyo Nov 1 and departing from KIX Nov 12. What is the best way (route) to see Kyoto, Nara, Mount Koya, Osaka, Hiroshima and Miyajima. Not necessarily in that order as I have the option of arriving in KIX and departing Tokyo if that would work better. Am flexible on time spent in each location. Thanks.

Not sure where you're coming from. That might impact your choices of flights. (And possibly open up other options such as routing via ICN to reach airports in Western Japan).

Unless you have to visit Tokyo, arriving and departing KIX might be just as good, since all of the locations that you want to see are in West Japan.

To plan the itinerary, I'd recommend that you check JNTO's site and see if there are any festivals in those places during your stay. Another consideration is that weekends will be more crowded on Miyajima and in Kyoto, since many people will be there to see the foliage.

The order in which you listed the places seems like a fairly logical order to visit them, but it makes sense to adjust that if you find a festival you want to see or if you want to be in Miyajima and Kyoto midweek.