5 days in Kyushu in October 2019

Ive read all the really helpful posts so far about 5 day trips to Kyushu and have noted all the suggestions re temples and parks which I will include in my itinerary.
There are 3 of us non Japanese speakers but we have lived and travelled in Japan.We will start in Beppu to get acclimated and see some rugby(?)and then plan to hire a car for the trip to do Kurakawa onsen and Mount Aso. Which ryokan should we stay in there- Seifuso has been suggested?
Is it worth going to Kumamoto altho the Suizengi gardens look fantastic ( worth visiting in late October?)or should we head to Nagasaki ?
Is it worth going to Hirado? We are looking to do some cycling and or walking so where is best for that.on the way to Fukoka we will visit the pottery towns- any recomendations?
Finishing in Fukuoka and again have taken note of all the really helpful suggestions
What am I missing bearing in mind it will be late October?

You've listed a lot of places for 5 days.

Since you are starting at Beppu. And including Asosan and Kurokawa. Places like Hirado at too far away. Stick with central and eastern Kyushu.

Since you'll have a car, hit the places which are difficult to acess with public transport. Eg Tachachiko.

Close to Beppu is Yufuin. So that is almost 5 days in my suggestions.

You may have some other thread somewhere but I just don't have the time or energy now to find it.
Suizenji in Kumamoto is indeed very nice but given the castle's current state of repairs, it would make far more sense to go see Nagasaki - there is enough for a day or two of absolutely top-notch sights. Not to mention there is also Sasebo, Unzen, the Bio-park, and Huis Ten Bosch to see if you wish. Hirado would be good if you have an interest in the Christian history there. Otherwise, given its remote location, your time might be better spent elsewhere, especially closer to Saga and Fukuoka since that is where you are going to end up.
If you have not seen it, the Yutoku Inari Shrine is simply stunning to see.
https://youtu.be/2UU_1Aip_l4

After you drive around Beppu, Yufuin, Aso, Kurokawa, Takachiho, and/or Usuki (don't attempt them all unless you want to spend most of your 5 days doing it), you should park yourself in Fukuoka and get a N Kyushu rail pass. You can take day trips as far as Nagasaki as well as points between.

Okawachiyama is a nice pottery town in the mountains. You would have to take a short private railway line from Arita to Imari, and then a bus/taxi to the town.
https://www.japan-guide.com/e/e8303.html

If you want, you could just go as far as Arita to check out some kilns, shops, and the pottery museum.
https://www.japan-guide.com/e/e8302.html

You could also go to Karatsu for pottery and a castle, see the Nanzoin temple with its large reclining Buddha at Sasaguri Town, check out pottery and the old town in Hita, Yoshinogari or the Yutoku Inari shrine in Saga, and if you want, take the Kyushu Shinkansen down to Kumamoto (the pass doesn't get you to Kokura except by local). You can walk around the outside of the castle to see the damage and the work, but you can't go into the main donjon or the Hosokawa mansion area yet. You can also check out the Craft Center as you make the loop, and walk over to the Lafcadio Hearn house off the arcade.

There are also the boat rides through Yanagawa, and the historic site at Dazaifu.
https://www.japan-guide.com/community/mfedley/report-2676
https://www.japan-guide.com/e/e4850.html

By basing yourself in Fukuoka, you wouldn't be hauling your luggage from place to place. An early start from Hakata Station can even get you to the Gunkanjima (Hashima) tours in Nagasaki on time.
https://www.japan-guide.com/e/e4414.html

October is a nice month. It can still be hot and humid, with an occasional "taifu," but the heat of July/August should be past. You can go anywhere unless a heavy rainstorm soaks the tracks.