Mount Koya, hands down. A distant second would be the Myoshin-ji subtemples. Don't bother with Enryaku-ji, it's not worth it despite the World Heritage status of the temple itself.

I know that the Kyoto tourist information center has a handout with a list of shukubo (temple stays) in Kyoto City, but I don't have a digital copy handy. There are a couple in Kyoto that I heard good things about besides Myoshin-ji, but I have forgotten their names.