If you know the story so Sakamoto Ryoma well enough, you would probably already know that it is said he was the first Japanese, along with his wife, Oryo, to go on a honeymoon. He did so in Kirishima and the park is one of the place he visited and where he had a bath in the onsen.
While walking in the small park, you will see a statue of the couple as well as many mentions of their names, that you will notice if you can read Japanese. You can also get down the stairs and get a nice view on the river.
In the park you will also find a small museum with an entry price of 300¥ and onsen for 420¥. They also sells souvenirs, onsen tamago (hard boiled egg cooked in the onsen water) and soft serve ice-cream.
There is also a staircase in the back of the park that will lead you to a really small shrine called Ryoma-jinja. I did not go much further, but there is a trail going in he forest. I am not sure where it go or how well it is maintained. If it the old Olle trail (it was the end point of the trail), I have been advised to not use it at the risk of getting lost in the forest, so it might be wiser to inform yourself on he current status of the trail before committing to the hike.
The onsen is quite simple with a single bath, but it is still relaxing to get in the hot water. I decided not to visit the museum so I cannot really say if it’s worth the price, but I would get ready for it to be in Japanese only.
While neither the park or the onsen absolute must see, if you are in the area, especially with a car, and that you like Sakamoto Ryoma, it is for sur a nice place to stop.