Mount Rokko is the tallest point in Kobe’s resident mountain chain. While most visitors access the top of the mountain via the auto road or a cable car, there is also a trail across the ridgeline with stunning views of Kobe and Osaka Bay. For a nice run without too much tough climbing, we recommend starting at the Rokko Terrace Garden and heading east. The views are great and the path is smooth (but a bit narrow), with minimal obstacles and elevation gain. It’s about 3 km (one way) from the Terrace Garden to the “true summit” of Mount Rokko.
There are numerous other running/hiking options in the area, shown in this trail map, including an ascent from Ashiyagawa Station.