18 Days alone in Japan itinerary

I'm travelling alone next April to Japan for 18 days and just planning the trip is an adventure on its own! There so much to see that I've made like 10 versions of the itinerary and I'm still trying to decide what to do. I ended up with two options that are not that different from each other, and I'm sure some of you can recommend me the best one or even give me some alternatives that might be better.

To start with, the musts. I want to spend some quality time in Tokyo exploring culture, food, music... And I've put 4 full days in Kyoto including a day trip to Nara, but not sure if that would be too much time. Apart from the big cities, I really want to go to Yakushima, Koyasan and Kojima, as I'm a denim enthusiast and I want to spend some hours there shopping good quality Japanese denim.

Then I've tried to accommodate more places based on that, and that's when I started to have some doubts. Mainly, I'm choosing between a day in Osaka or Hiroshima or Miyajima. I think I have time to briefly visit at least two, but it might be all too rushed, I don't know. Is it worth to visit Osaka for just one day? I've heard great things about food there. And Miyajima looks beautiful but I feel Hiroshima is an important city to visit for obvious reasons. I know is a pain to get to Yakushima and that has been part of the issue but I really want to explore a bit of the island, even if that means missing some important landmarks. This is definitely not going to be my last trip to Japan after all.

I'm really open to suggestions of more interesting places, and if you think there are parts that are difficult to achieve I'm all ears. Here I included two versions of my itinerary. What do you think? Thanks for your help in advance! :)

DAY 01. W 05 APR. Flight from London
DAY 02. T 06 APR. Arrive to Tokyo in the morning
DAY 03. F 07 APR. Tokyo
DAY 04. S 08 APR. Tokyo
DAY 05. S 09 APR. Tokyo
DAY 06. M 10 APR. Day trip to Nikko. Night in Tokyo.
DAY 07. T 11 APR. Tokyo – Koya-san
DAY 08. W 12 APR. Koya-san – Kojima – Hiroshima
DAY 09. T 13 APR. Hiroshima – Yakushima
DAY 10. F 14 APR. Yakushima
DAY 11. S 15 APR. Yakushima – Miyajima
DAY 12. S 16 APR. Miyajima – Kyoto
DAY 13. M 17 APR. Kyoto
DAY 14. T 18 APR. Kyoto
DAY 15. W 19 APR. Kyoto
DAY 16. T 20 APR. Day trip to Nara. Night in Kyoto.
DAY 17. F 21 APR. Kyoto – Tokyo
DAY 18. S 22 APRL. Tokyo – London
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DAY 01. W 05 APR. Flight from London
DAY 02. T 06 APR. Arrive to Tokyo in the morning
DAY 03. F 07 APR. Tokyo
DAY 04. S 08 APR. Tokyo
DAY 05. S 09 APR. Tokyo
DAY 06. M 10 APR. Day trip to Nikko. Night in Tokyo.
DAY 07. T 11 APR. Tokyo – Koya-san
DAY 08. W 12 APR. Koya-san – Osaka
DAY 09. T 13 APR. Osaka – Kojima – Hiroshima (Miyajima)
DAY 10. F 14 APR. Hiroshima (Miyajima) – Yakushima
DAY 11. S 15 APR. Yakushima
DAY 12. S 16 APR. Yakushima-Kyoto
DAY 13. M 17 APR. Kyoto
DAY 14. T 18 APR. Kyoto
DAY 15. W 19 APR. Kyoto
DAY 16. T 20 APR. Day trip to Nara. Night in Kyoto.
DAY 17. F 21 APR. Kyoto-Tokyo
DAY 18. S 22 APRL. Tokyo – London

Tokyo to Koyasan is a LOT of travel. Break it up by spending a night in Osaka first. Likewise, Koyasan to Hiroshima is also a lot of travel. Consider putting Kyoto in between.

Hiroshima to Yakushima is also quite a long day, particularly if you take the ferry. You could fly from Osaka to Yakushima (or Osaka-Kagoshima-Yakushima) instead.

I would put Yakushima just before returning to London. Then, fly from Kagoshima to Tokyo. So, something like Tokyo - Kyoto - Hiroshima/Miyajima - Osaka - Koyasan - Osaka - Yakushima - Tokyo. Stops you going back and forth too much.

Yakushima is the main destination making your itinerary awkward, as it's quite far from the other locations (on the opposite end of another island!).

Darn hard to improve upon the advice offered by sq (guest). Best tip is leave for Koyasan from a nearby city like Osaka or Kyoto so you get there with plenty of time for the long bus ride and stroll through the old cemetery en route to the stayover monastery.
There is no such thing as too many days for either Kyoto or Tokyo. Osaka kind of depends; the Castle isn't the real McCoy but Sumiyoshi Shrine and Shittenoji Temple are very much worthwhile...and relatively easily included on excursions out from Nara or Kyoto. Of course if you're into theme parks and exciting entertainment districts then Osaka becomes a bit more compelling.
Miyajima pairs well with neighboring Hiroshima; stay in Hiroshima and take a long half a day to go to Miyajima. And the mandatory okonomiyaki which must be eaten by all foreigners anywhere west of Nagoya will be, in my opinion, even better, Hiroshima style than Osaka style. Think baby oysters just out of the Inland Sea.
I take it you're going all the way to southern Kyushu...good move. I need to try this some time. Nagasaki/Deshima/Chinatown is awesome and despite the quake damage, I've heard nothing but good about Kumamoto.
Do your island on a subsequent trip. And plan on the reality that you are going to have two or three half-days when you will have to stop and rest up, go get money from your credit card at a bank where they are required to conduct all transactions in Japanese (so look for the sign offering a bank employee who speaks English to translate for you), and, my favorite, become acquainted with the coin laundry at your hotel.
Have a great trip; my second was 22 days and I've never regretted it as now I'm down to cramming the entire trip incl. flights into 10 days. Gampai!!!