Going back to Japan – 1 week at Kyushu Itinerary (mainly Yakushima question)

Hello all,

I wanted your thoughts on my itinerary to Kyushu. I will be traveling there for 1 week as part of my trip. My current itinerary is

Fly in to Fukoka > Fukuoka > day trip to Nagasaki > Beppu > Kagoshima for 3 nights > fly out of Fukoka

My main concern is during my time at Kagoshima, I want to visit Yakushima for a day trip. There is a ferry that arrives at Miyanorua port (Yakushima) at 9:30 AM and last one departs at 4 PM. I would love to see the rest of the island but the main reason for visiting is to hike the Shiratani Unsuikyo to Taiko Iwa which is 3 mies. There is a bus that leaves Miyanorua at 10:15 AM and Shiratani Unsuikyo at 2:20 PM. On paper it seems to make sense, but I wanted to ask if **anyone else has done the same thing .**

I really wouldn’t prefer to rent a foreign car in a foreign country with foreign language, but if I do would likely stay overnight at Yakushima. **How is driving around Yakushima?**

Thanks!