I recently checked out an incredible place to stay in Kyoto: the Ayanokoji house offered by Aoi Kyoto Stay, a company that specializes in renting refurbished Kyoto houses. You can find a link to their site here. The house is in a lovely restored kura (storehouse) right in downtown Kyoto on the quiet Takasebune Canal. It's just five minutes' walk south of Shijo, but it feels like worlds away. It would make the perfect base for exploring Kyoto.
Here's a picture of the house from across the canal:
Here's the living room, with a view of the canal:
There's a record player and a collection of great records (as well as, of course, an iPod dock):
Here's the simple kitchen: