Where to stay in kyushu outside of cities

We have a 2 week itinerary in Kyushu planned out but I'm less familiar with which smaller towns to base ourselves in on a road trip itinerary.
After Nagasaki, we want to visit Nagasaki Bio Park, Huis Ten Bosch, Arita, Mifuneyama Rakuen, Yutoku Inari Shrine. Should I be looking at Takeo and Ureshino onsen? This would be 2 nights.

We plan to stay 3 nights in the Aso area to have a full day around Mt Aso and Takachiho each. I realize we could stay in Kumamoto but that seems like a lot of extra driving. I see there are places mainly north and south of the park and west towards the airport. Not sure if it makes a difference? We would be heading towards Yufuin/Beppu after.

Specific accommodation recs appreciated or just where in general might fit well!

If you want to see Mt Aso and Takachiho an accommodation in MinamiAso (somewhere along the Minamo Aso railway line valley would make sense. There are many accommodation. I would definitely not stay in Kumamoto for that. Traffic out of the city is quite terrible and it�fs much nicer to stay in the countryside. This assumes you have a car. Public transport in this area exists but is scarce. If you need to rely on public transport then probably Aso city is your best choice.

North or south Aso makes sense. Just note south options may not cater well to international visitors. Really need to do homework on these options.

I see no reason not to stay at Yufuin. Not a city, and if you pick a hotel slightly outside the touristy trap area, it's almost a rural stay.

You can find hotels both on Google maps and hotel dot com very easy for research purposes for Amy location.

I think around Aso, we will likely just look for a hotel and then hopefully try to stay in ryokan in the Saga area and Yufuin in between. It does seem like more of the hotels are clustered in the northwest area of the park so helpful to know that minami aso and the southern half don't cater to international visitors as much.

Any specific accommodation recs in Yufuin?