Kirishima Jingu is a large Shinto shrine on the lower slopes of the Kirishima Mountains, a group of volcanoes in northern Kagoshima.
The current buildings date back to 1715, though the shrine used to be located higher up in the mountains where it had been destroyed by volcanic activity multiple times.
The main kami enshrined here is Ninigi, the grandson of the "sun goddess"Amaterasu and ancestor of Jimmu, the mythical first emperor. The shrine was originally located at the foot of nearby Mount Takachiho, according to the ancient myths the site where Noinigi and his heavenly entourage descended.
There is another Takachiho, much further north in the mountains of Miyazaki, that is now considered to be the site where Ninigi descended. When the Meiji government decided that it was a great shock to the people of Sastsuma, present day Kagoshima, home of the "other" Takachiho.
National myths in Japan largely came about by government decree in the late 19th Century. Prior to that the imperial family had a set of myths, but so did the major clans of ancient Japan as well as the myriad tribes that inhabited the Japanese isles. Basically the imperial families versions of the myths are the ones now touted as national.