Well i havent been there and i haven´t tried it and maybe its not your thing, but if you´d really save money you could try Hitchhiking. There a Site with links and stuff here:
Hitchhiking Japan in East Asia - Backpacking and Budget Travel | digihitch World
For overnight stay you could try couchsurfing (i´m not sure how many are there in Japan)
CouchSurfing - Site Down Message or
Free Accommodation world wide through Hospitality Exchange - Hospitality Club
If you intend to stay more than 2 weeks at a place and want to safe money you could try wwoofing
http://www.wwoofjapan.com/main/ (this will probably take more effort and time, but end up giving you 2 extra weeks in a Japanese Home/Farm/Inn for free (you will work some Hours a day for Food and Accomodation, check out some off the offers).
Well thats as far as i got till now for cheap travel / Room. Some stuff may take some more time, but you may consider it interesting, thats why i posted this stuff. I will be going to Japan for 1 year Working Holiday, so im collecting usefull link right now
Firebird