Indoors is nice, but Koya-san's most famous sights are outside... including more Buddhist images than you've ever seen in your life. Normally they're not piled up in a mountain like this...
Something you rarely see: the traditional Japanese-style kitchen for a Japanese Buddhist temple. Nowadays they apparently only use it when the temple has a big meeting of monks and they have to feed a lot of people. Nothing wrong with the facilities: they just normally have stuff piled up in the way and it’s a hassle to clear it out of the way! Note the chimney, rare in Japanese buildings - in most traditional structures, they let the smoke go up into the thatched roof to ward off insects.