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Hello folks,
I have already visited the classic "tourist route". We were in Tokyo, Hakone, Kyoto, Osaka and Kobe.
This year we want to visit the southwest of Japan (Kyushu and Chugoku) in September.

So this is our plan so far:

1. Day: Arrive at Fukuoka by plane

2. Day: Explore the City

3. Day: Daytrip to Dazaifu

4. Day: Buy the All-Kyushu-Railpass and do a daytrip to Nagasaki

5. Day: Leave Fukuoka by train and travel to Kagoshima

6. Day: Explore the City of Kagoshima

7. Day: Daytrip to Ibusuki

8. Day: Leave Kagoshima early in the morning towards Kumamoto. Place luggage at a coinlocker and visit the City. Travel to Aso in the evening. (End of Rail Pass)

9. Day: Hiking at Aso

10. Day: Not sure yet - maybe Daytrip to Kurokawa Onsen?

11. Day: Leave Aso towards Beppu - stay there at a Ryokan

12. Day: Explore the "Hells of Beppu" and the City - and some SPA at the onsen of course

13. Day: Leave Beppu towards Hiroshima

14. Day: Explore the City of Hiroshima - Peace Park/Museum and so on

15. Day: Visit Miyajima Island

16. Day: Daytrip to Onomichi - rent a Bike there and ride the Shimanami Kaido Cycle Route

17. Day: Leave Hiroshima towards Osaka

18. Day: Daytrip to Himeji

19. Day: Shopping at Osaka

20. Day: Fly home


ThatLs the plan so far - what do you think?
I also have some additional Questions:
1. Do you think it is essential to stay overnight at Nagasaki - The problem is the long and complicated travel to Kagoshima from there
2. Is one day enough to visit Kumamoto?
3. Do you think it will be a problem to do this Route only by public transportation?

ILm looking forwards to some answers! Thank you!

Itinerary is good.

Not sure the JR Kyushu pass will pay of though? Have you done the calculations?

Not too rushed, doable with the trains easily enough, you get to do a lot. Loos fine. You might do Himeji on the way to Osaka.

Looks good. Agree on Himeiji as stop over between Hiroshima and Osaka.

For the Shimanami Kaido part either you are a very avid cyclist to do the whole route as a daytrip from Hiroshima (youfll need to return the bike by a certain time. ) or you just plan to do a part of the ride. Which is fine.
I would highly recommend to reserve the bike before you go and would recommend to avoid WE.
September can also be still quite hot so take it easy and a lot of water.

Kumamoto 1 day sounds enoughto me. Frommemory there is one nice garden and the castle. Not sure if it reopened yet. But either way doable within 1 day

I think it works pretty well. You do need to work out the details more about travel around Aso and getting to Beppu by bus or train, if you are not renting a car. Buses are not that frequent; distance wise it's not that far, but it is rather time consuming. Plus there's the question if the crater rim area will be open then. Currently it is closed off.
It is not essential to overnight in Nagasaki - but if the weather is good and you have the time, the night view from atop Inasayama is spectacular (called the "ten million dollar view" for a good reason). Be sure to try the chanpon and saraudon while there.
I'd say a day for Kumamoto City is fine. Both the castle and Suizenji are very good. For other places, it depends on your interests, but I didn't find too much else that held great appeal to me. If you go to Kurokawa, be sure to get the tegata and visit 3 places there - some places are very good while others are just meh - but all cost the same with the tegata so choose the better places like Yamamizuki and Hozantei. Be aware also that the place is quite spread out.
https://www.japan-guide.com/e/e4575.html
For Beppu, the Hells Tour only takes a few hours - you could also go to Oita City and see Takasakiyama with its hundreds of macaques - it's one of the better places for them in Japan. Five of the Hells are very close together while 2 others are more apart. If you see all, check and see the next eruption time for the Tatsumaki geyser so you're not waiting around 35 minutes for it. Get the pass for 2200 yen if you're going to see all of them.
If you do the Shimanami Kaido, while on Ikuchijima, go see the Kosanji Temple. It's wildly ornate and just amazing.
https://goo.gl/Q843Bg

Looks good, just a tiny addition or two to the already good advice here.
When you do the shimanamikaido, you could just do part and get the ferry back.
e.g. from Setoda to Onomichi
https://s-cruise.jp/cruise-eng/setoda-eng/
Doing the whole thing in one day is quite the undertaking unless you're a very keen cyclist.

We are just finishing our 3rd trip to Japan, spread over 8 weeks.

Onomichi is our favourite place we have visited so far in Japan.

If you are doing the Shimanami Kaido in a day, you wonft see anything of Onomichi other than the ferry port and the cycle pick up.

As others have said, if you are reasonably fit or hire an e-bike (and have reservations in advance), the whole bike trip is fine to do in a daycbut itfs still a long day and you will miss a lot on the way and wonft get chance to see Onomichi properly.

Itfs tough as there are so many options.