Kōya-san (高野山) is a raised tableland in northern Wakayama-ken, covered with thick forests and surrounded by eight peaks. The major attraction here is the Kōya-san monastic complex, which is the headquarters of the Shingon school of Esoteric Buddhism. Though not quite the Shangri-la it's occasionally described as, Kōya-san is one of Japan's most rewarding destinations, for the natural setting of the area and the opportunity to stay in temples and get a glimpse of long-held traditions of Japanese religious life.
Keep in mind that Kōya-san tends to be around 5°C colder than down on the plains, so bring warm clothes if you're visiting in winter, spring or autumn.
Whenever you go, you'll find that getting there is half the fun – near the end of its journey, the train winds through a series of tight valleys with soaring mountains on all sides, and the final vertiginous cable-car leg is not for the faint of heart.