The Okuno-In is a huge cemetery sheltered by cedar trees. It is the most beautiful place in Koya-san. There are many jizos, or ancient tombs, but also many more original ones, such as the monument funded by an insecticide company in memorial to all the termites they have exterminated. There is a something uniquely Japanese about the atmosphere of the place.
There are also 5 large temple complexes to see in the city, each with its particularities: pagodas, museums, etc. It is possible to participate in an introduction to Buddhism, with the delivery of a certificate at the end of the session.
If you have the time, go to discover the surroundings and the pilgrimage trails which cross Mount Kii.
You can find articles about my latest visit to Koyasan on my personal website.