Rather than searching the web by using "cheap hotels Japan" or someother phrase, it is much handier to use one of the services like Rakuten or Yahoo! Japan to book your hotels. I have a Yahoo! Japan login, which I have used to book hotels online in Japan for the last 5 years. It works like a dream. You do not need a credit card.
There is a difference between 旅行 and 出張. Shuccho are usually business hotels, and maybe accomodation only or the option to add meals. Ryoko usually denotes pleasure and may well be ryokan or other weekend kinds of places.
Of course, these days you can also use Travelocity to make reservations in Japan. I have done that many times and never had a problem.
Don't forget if you are stuck, you can always purchase a "night pack" and stay overnight at manga kissaten or some of the saunas. Capsule hotels are more expensive than day laborer type hotel rooms, but many drunk people who miss their trains choose to stay at capsule hotels. I stayed at one that was almost empty at 11 pm and completely full by 4 am.