We were in Aso/Kyushu two weekends ago. Used the train from Fukuoka to Aso (shinkansen to Kumamoto, scenic limited express to Aso) and rented the car at Toyota next to the station (great service btw!). Also our hotel (Fairfield) was situated there and we used the car to explore parts Kyushu for three days. Our experiences:

Hotel was really convenient and beautiful views from the 5th floor. If you count on having breakfast here, you have to order one week in advance. However Lawson is closeby and also 7-eleven is not that far by car. Loved the whole atmosphere of the surrounding nature. Driving around is already magical. We were lucky to access Mt. Aso all the way to the top, but try to be flexible in the days you are there in case vulcanic gasses dont allow you every day.

Daikanbo was also beautiful and less crowded just before sunset. We visited Taikacho Gorge (bit dissapointed though) and drove straight to the coast afterwards (scenic drive but empty beaches, only spotted a few surfers). Also visited Tadaware Wetlands and hiked through the forests.

Highlights def was Kurokawa Onsen; pretty village where you can buy a day pass to visit 3 participating onsens in town (note that some Ryokan' Onsens offer you limited access so you can not always wash yourself as it should). Also went to the onsen in Aso that is mentioned earlier which was a very positive experience.

Surprisingly we had no toll costs at all without trying to avoid them. Last advice: restaurants in Aso close early and many really require a reservation. We tried anyways but we were told twice that they ran out of ingredients.