Kimi Ryokan has been a traveller favourite for decades and it's easy to see why: the tatami rooms and shared bathrooms (including a Japanese cypress bath that can be used privately) are clean and well kept; the service (in multiple languages) is gracious and helpful; and there's a lounge and a rooftop terrace. Oh, and the eminently reasonable price. Book well in advance.
Kimi Ryokan
Shinjuku & Northwest Tokyo