There are many sources of information on budget hotels in Japan.

You can try TripAdvisor for candid evaluations of hotels in every price range, as well search "name of city"+"business hotel" on Google.

Thanks to TripAdvisor, I found a quirky business hotel (funny-looking statues out front, Japanese, Chinese, and Western food on the breakfast buffet; free Internet in the lobby, an open lounge area) near Osaka Namba Station for my last night in Japan on a trip a couple of years ago.

In 2006, I was scheduled to attend a meeting in a city so obscure that even Toyoko Inn hasn't gotten there yet, and Google led me to a decent-looking business hotel. Unfortunately, the trip didn't take place, but should I ever need to go to that city, I'll know where to stay.

The Japan National Tourist Office used to have a pamphlet that listed mid- to low-priced hotels and ryokans that welcome foreign visitors, and the list of cities covered was quite extensive. You may want to ask and see if they still publish that pamphlet. Another option is to go to their website, download the pdfs about the different cities and regions, and check out the lists of hotels and ryokan there.