I stayed one night in the Rengejoin Temple in Koya-san, and it was one of the highlights of my trip to Japan.

Koya-san is a mountain south of Kyoto/Osaka, and is considered one of the holiest Buddhist shrines in Japan. There are over 100 Buddhist temples on Koya-san, and many of them accept tourists. I chose Rengejoin Temple because I had read that they were especially well-equipped for foreigners, and indeed, most of the guests were from Europe and the US. This did not make the visit less authentic, however, since this is a functioning temple, just more accessible for those who do not speak Japanese.

The price includes the room, dinner (which was excellent) and breakfast. It is also possible to attend evening and morning prayers (with a brief explanation in English by the chief priest), which allowed for a fascinating insight into Buddhist practices.

The only possible drawback is the price. It was relatively expensive given the location (about 9,000 yen per night), and there are certainly cheaper temples on Koya-san. That being said, the money has been invested in the temple, which is kept up in impeccable shape (including breathtakingly beautiful gardens).

I highly recommend Rengejoin.