A 24-day trip is generally an enviable amount of time to travel for most people. And certainly enough to add a couple days for Ishigaki, if you wish. Although nearly 4 days is more than enough - you could easily take the ferry and add in Taketomi, and if you want to see other islands (Miyakojima, the main island, etc) you could use the Okinawa Island Pass for cheap fares between the islands.
https://www.churashima.net/jta/company/islandpass_en.htmlThe confusing part of your plans is getting there - you'd need to return to Tokyo after Nagano first. There are some direct flights on cheap fares for example on ANA's Experience Japan Fare.
http://ana.ms/20Xtf8tFor the rest of your trip, you could add another day trip from Tokyo since you are putting in 8 full days in the area. As for going to Himeji, it will take nearly 4 hours, but there are some direct Hikari trains in the morning where you wouldn't need to transfer. The castle is of course the crown jewel, but don't miss the beautiful Kokoen Garden there as well. If you still have time, you can also see Mt Shosha.
https://goo.gl/65ZtRiFor Hiroshima, don't shortchange yourself by just seeing the Peace Park - there is a lot more, and the crowds usually don't go there much - such as the Shukkeien Garden and Mitakidera Temple.
https://goo.gl/fAz4axYour timing for Miyajima is excellent - you'll be there just before they cover up the big torii gate for renovations (12+ months). Be sure to see the shrine at high and low tides as well.
http://www.tides4fishing.com/jp/hiroshima/itsukushimaThe shrine will take less than 30 minutes easily. Don't miss the Daishoin Temple also - it is in many ways even more beautiful. The next morning, you could also fit in Iwakuni just south of the island. Nicest old bridge in the country.
https://youtu.be/0COOZXi66mMOne thing missing in your Kansai stay is seeing Nara. Very worthwhile. If you are pressed for time, you can concentrate on the Nara Park area and see it in about half a day.
https://goo.gl/LfvWnLYou could also go see Osaka or Kobe in the evening after a day of sightseeing in Kyoto. For Koyasan, you might bring some snacks with you as well - some people get hungry in the evening after the Buddhist vegetarian food, which is very light. If you wish to see the Okunoin cemetery at night (a truly surreal experience), be sure to pick a temple with *no 9 PM curfew*.
https://awesome-tours.jp/en/tour/night-tour-return-bus/You don't need any tour through it though - you can just go by yourself.
A 14-day JR pass would pay off well for you (except for Koyasan, the Alpine Route) but there are regional passes for them. For day trips in Tokyo, there is the Nikko Pass or Tokyo Wide Pass.
From mid-May you may be able to see some beautiful irises as well as hydrangea - for the latter especially, Kamakura (Meigetsuin, Hasedera Temple etc) are good and in Kyoto, there is the Yoshiminedera Temple.
Hope it all goes well for you.
