A friendly taxi driver from Ishigaki introduced me to two places for watching the sunset.
One is the Firefly Observatory (ホタル滝展望台) in Banna Park (バンナ公園). Every year from April to May, you can watch the sunset and enjoy the large fireflies. Of course, in order to prevent mosquitoes but not to fireflies, you need to wear a long shirt and long trousers. But in the winter, due to the location of the sun, it is not suitable for sunset.
Another location is the Southern Gate Bridge (サザンゲートブリッジ). This bridge is connecting the artificial island to Ishigaki. There is a platform in the center of the bridge. Many people will watch the sunset there. The latter is not far from the hotel I live in. I walked to watch the sunset more than one day, and the scenery was really good.