The temple experience par excellence is Koyasan, in Wakayama-ken southwest of Osaka and reachable by Nankai Railway from Osaka's Nankai Namba station or by a roundabout JR route, if you have JR passes.

You make a reservation through the central booking agency (most guidebooks have the phone and fax numbers; they probably have e-mail nowadays for all I know), and the agency assigns you a temple depending on space available. When you arrive at the end of a very scenic journey, the last leg of which is by private railroad, you go to the booking office in the station and they give you bus directions to "your" temple.

The rooms and prices are like those of a mid-class ryokan, although without private bath, and you are served an ample vegan dinner in a common guest dining room. There may be a lecture on Buddhism (in Japanese) during the dinner. The only uniform religious requirement is that you attend their 6:00AM service. Since there is really nothing to do in the evening, you may as well turn in early. Even if you speak Japanese, the service is rather tedious, because it consists of the monks chanting in the Japanese pronunciation of classical Chinese. But it's a small price to pay. After an ample vegan breakfast, you are free to explore the other temples and the small town that exists to serve the temples and their visitors, as well as the cemetery and the tomb of Kobo Daishi.

I went the roundabout JR route from Osaka to Koyasan to Nara, and the trip took a couple of hours each way.