Ragtime is the ideal jazz cafe in many ways. It's a small place up on the 3rd floor of a building right next to Chitose-Karasuyama station on the Keio Line, a residential part of the western outskirts of Tokyo. A small square room with about 20 seats, the feeling is cozy and inviting from the start. There are pencils and strips of paper on each table for customer requests, always a sign of good vibes. They say only one per customer, but when I went there as a student several years back, spending 3 hours "studying" in the place, they took all my repeated requests. All genres represented, and mostly vinyl behind the counter, of course.
If there's a city other than Tokyo in which you can find such wonderful jazz cafes in a random western outskirt..well, let me know! Ragtime is another hidden gem that confirms Tokyo as the world's best jazz town.
Good photos of the place and a map on the single-page website.