Located near the onsen area of the town, you can find Oshidorino Pond. While the pond is not big and there is a walking course that goes around.
The walk around the whole pond is 2,7 km. Walking around and back to the onsen area should take less than an hour. There is not much incline on the whole path, this will make an easy walk if you have some spare time.Some parts of the path are in the forest while other parts will offer a view on the lake. During my walk, I only saw a couple of people, so it should also be a quiet walk.
On the other side of the pond, you will find a torii gate and if you take a few minutes to go down that path, you will find a carving of Daikokuten, the lucky god of wealth and commerce in the rock. It is unknown who did he carving or when. In summer you can also see hydrangeas blooming.
The pond is actually an artificial lake and you will see the dam that contain the water when you reach the western side of the lake.
If you are interested in a longer walk, there is a hiking path on the east side of the pond that will lead to the intersection of road 57 and 389, near the golf. From there you would have other options of trails to use or return to Unzen following the road.
If you want to have a view from a higher elevation, you would be better choosing a different trek and there is different mountains that you can easily climb at walking distance from Unzen, with various length and difficulty level, so for sure you have different options even if you do not want to take a but to a different area of the national park to hike.