Can anyone help me on cheap places to stay during my 2 months in Kawasaki-shi Japan?

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I am going to spend Kawasaki-shi Japan for 2 months and I want to rent a place to stay for 2 months like a cheap vacation home or a small apartment. I am going to be visiting my boyfriend but I do not want to stay with him because of our religion. Does anyone know about cheap rental places in Kawasaki-shi Japan? I am flying from Vancouver BC Canada. Travel info is welcome but I need information on cheap places to stay in Kawasaki-shi Japan. Thank you!