Beside ryokans, you'll have to stay at tube hotels. Cheap and it's an experience you'll never forget. Travel by train and buy your train pass in your home country = much cheaper ! Japan is not as expensive as people say, just spend your cash wisely ;) about 6 years ago
Actually, there are many more options than there used to be. We found quite a few very economic backpacker type accommodations, perfect for a family, even in the middle of Kyoto and further south in Beppu.
(see my other answers on Kyoto for links)
Also, they might be boring, but we found business hotels were impossible to beat for value: simple, clean and ultra efficient for as little as $40 a night for a room.
Not a capsule in sight. about 6 years ago