This is an excellent running path for anyone in Kagoshima Prefecture - I was pleasantly surprised at the end.
If you're coming from Kagoshima City, go to the number two platform at the bus terminal and take the bus all the way to the end (if it's going to the interchange, get off about two stops earlier). It's about 30 minutes.
You're in Yoshino Town. Take Highway 220 (not even really a highway, just a country road), and follow the signs. This is a beautiful route, but rather hilly going out to Terayama; it could be worse, but be prepared to question your sanity.
If you do keep it up past the twists and turns, you'll eventually find yourself in a dark wood, where the straight road is lost...
No joke. You'll end up on a road surrounded by a dark thicket of trees and bushes until you finally see a light at the end of the "tunnel".
A small parking lot, and a platform leading all the way out to the edge of the mountainside.
This observation point gives you some spectacular views of Kinko Bay, Sakurajima, and Kagoshima City.
This photo was actually taken from Yoshino Koen, and the views are similar - nevertheless, Terayama gives you almost 300 degrees visibility at a higher altitude: an excellent place for an early morning or evening run to catch the sun on the horizon. The view of Sakurajima is quite amazing.
There are some vending machines along the road with water, but nothing at the park. Strictly speaking, the park is some distance away; I couldn't find it.