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