Guest House Makuya
Of the places I stayed in Japan, one of the most Authentic and enjoyable was the Guest House Makuya. But since room prices start at $41 per night including use of communal bathrooms and kitchens, I would say it is well worth it for the value, too.
(Images borrowed from lastminute.com.au.)
As you can see in the photos, the place offers you a very traditional sensation of Japanese culture. But I would say the style is more wabi-sabi and similar to a hostel atmosphere than you would find in most ryokans. A tip I will offer you is that you should travel light when you go. There is no stairway or elevator directly to the second floor, so all heavy bags will have to be carried manually up through that raised room in the middle and then up some traditional stairs. This is not the fault of anyone. It's just something you want to be careful about when you go. And it is so worth it. And the plentiful-ness of laundromats in Japan make it needless for you to take so much anyway.
The host was even nice enough to show me a collection of Japanese books and even samples of beautiful old fabrics.
The location is in the middle of a Kyoto district that is not too loud, and where there are bus stops near by, so travelling around town isn't too challenging. But since there are interesting things to see on each street, even going for a simple walk can be a pleasure.
If you would like to supplement your virtual experiences of Japan with real life, wearable objects, you could try perusing my online store. I try to keep my prices reasonable, and my products a blend of the fun and practical:
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