If you want cheap, you could stay the night in a "Love Hotel". These sound more sleazy that they actually are and I used them a lot when I lived there.
Most Japanese single people still live with their parents so when they want to spend quality time with their girl/boy friend, they go to "Love hotels" to rent rooms by the hour. After about 10pm the Room Rate drops significantly (as the singles have to go home) and can be a good place to stay.
We once got 6 people in one room after a heavy night in Osaka.
The Ryokan that are dotted around are also fantastic but some serve only traditional Japanese food including the dreaded Natto, fermented soy bean curd, and it is as bad as it sounds.