Jouyama is a very small mountain in Shirahama with two viewing platforms that look out over the Nojimazaki cape. The trail is quite short and easy to hike, but provides some beautiful scenery: from mountain passes, to outlook points, to tree-covered cliffs.
There are several possible entrances, but the easiest place to park is on the west end of the trail (marked on the trail map and the embedded map below). There are parking spaces along the side of the road, but they are poorly marked and easy to miss. You have to walk on the road at first, then follow signs for the path (labeled 城山遊歩道) which will lead you through fields to the entrance.
The path is not well maintained, and I definitely recommend grabbing a hiking stick from the stand toward the beginning of the trail. There’s a fork in the path here, so follow the stairs up to get to the first viewing platform. This part of the trail is a bit less perilous than the second half, and has sturdy wooden stairs to climb. However, the trail transforms completely after platform #1. To get to the second platform, you have to follow a tiny winding path with sharp drops on either side (this is where I found the hiking stick handy). The platform is little more than a shoddily-constructed metal frame, and the view is no better than from the first one. However, if you want to hike the whole trail, you might as well check it out.
After that, the path leads down the mountain to a temple where you can leave your staff. You’ll follow the road to the right through a charming residential farming area and past a couple more temples. After walking through a couple of fields, you will find another entrance to the trail that leads up some stairs to where the path forked off at the beginning.
You can see a map of the trail (Japanese) here: http://www.mboso-etoko.jp/top/photo/Lphoto/20100603133241066.pdf