An amazing combination of price, friendliness, and experience, Shunkoin (春光院 — Temple of the Ray of Spring Light) is definitely the place to stay. On my recent trip to Kyoto I spent two nights there and it was fantastic.
Located in a large temple complex, the Shunko Temple has two styles of rooms. Most of the rooms are just very simple carpeted areas with a futon in the center. For the cheaper rooms there is are two shared bathrooms and two shared showers. The more expensive rooms have beautiful hardwood floors, a futon (with a heating pad beneath it), a desk and chair, a private bathroom and shower. All rooms have a shared kitchen, which has all the modern amenities. Best of all there are bicycles free for the taking. While the accommodations aren’t luxurious they are more than adequate.
For a very small extra charge you can take part in a short zazen guided meditation. After the meditation you’ll be given a tour of the temple which is beautiful and rich in history. And after that you’ll be served delicious green tea. If you don’t know any Japanese you’ll be extremely comfortable here as the vice-abbot speaks English very fluently (perhaps more fluently than some American’s I know). The mediation and tour are both in English from start to finish.
The temple is located in northern Kyoto very close to Ninnaji, Ryoanji, and Kinkakuji. A short ways to the west is Daikakuji and Arashiyama. It is a few minutes away from a train station (¥190 to/from Kyoto Station) and there are bus stops everywhere. In short, the location is very convenient. While a stay in the central area of Kyoto may put you in a convenient location you’ll pay a lot more to be surrounded by noise and cement buildings. While the station and its surrounding area may be the center, it is just outside of central Kyoto that its real heart lies.
A stay at Shunkoin is a fantastic idea. It is a quiet, peaceful, friendly and cheap cultural experience.