Jamie D. Ducusin
Thanks to everyone for the helpful information!
Actually, after doing some of my own research I was able to find a VERY economical hostel located within a minute's walk of Kuramae station (on the Oedo Line, and according to the Hombu website, the dojo is just a 5 min. walk from Wakamatsu-kawada Station(Kawada-guchi Exit) on the Oedo Line).
They have both private rooms and dormitory rooms available:
Dormitory Room（8 people）- 2,800yen
Dormitory Room (4-6 people) - 3,000yen
Twin/ Double room - 3,400yen
Family ensuite room - 13,800yen
Well, this sounds good enough, but if you are really going primarily to train, I would recommend staying closer to the dojo. If you for example want to do 3-4 classes a day you will spend quite a lot of time (and money) travelling. If you are doing the morning classes, I am sure you will appreciate the extra half hour of sleep in the morning.
Prices for the Tokyo business hotel can be as low as (according to their website):
Quadruple: 16700 -> 4175 yen per person
Twin/double: 7200 -> 3600 yen per person
Single: 3980 yen
The little extra money you wold save on living far away is really spent on the subway anyway. I guess it all depends on how much you want to train. If you just want to drop in for a class or two it doesn't really matter where you live, but if you are going every day I would recommend staying within walking distance. Anyway, I think you will not find a very much cheaper alternative than the TBH anyhow.
Have a nice trip and good luck!