I would suggest staying at a ryokan if you can. I stayed at a couple of those last year and they were great:
Ryokan Kangetsu:
RYOKAN KANGETSU-Tokyo Budget Hotel-Economy Accommodation Cheap Inn Japan booking,
Homeikan:
http://www.homeikan.com/en/en_welcome.html
Those are both in the Tokyo area for a couple examples (not a very long trip to get anywhere around Tokyo anyways).