This place -New Koyo - is supposed to be one of the cheapest in town (
Economy Backpackers Hotel NEW KOYO ) but no idea if you get your own bathroom and toilet (probably not).
These are dirt-cheap capsule-type/makeshift backpacker inns in Tokyo and rest of Japan:
khaosan Tokyo Guest House ::Backpackers Hostel in Tokyo, Kyoto, Fukuoka, Beppu::
And, this place looks like it meets your budget but probably no ensuite bathrooms either:
Rates - toco. | Tokyo Heritage Hostel for Backpackers
This one has a double with ensuite bath/toilet etc:
Asakusa Ryokan & Hostel Toukaisou -- Cheap and traditional Japanese style hostel in Asakusa,Tokyo