Hiking

Yes, there is!

From Kinosaki Onsen Station walk down the main street towards the opposite end of town and Konotori no Yu bath house. The ropeway is across the street and river from Konotori no Yu. You can hike up to the top, starting from just behind the Kinosaki Onsen Shrine, or take the gondola.

Read more about it here: http://www.kinosaki-web.com/en/sightseeing/outdoor.php

But honestly, the best would be probably asking a local guide. They know every small detail that I am missing.. here is a list of guides in Hyogo where  Kinosaki Onsen is located.

https://triplelights.com/japan/hyogo/guides