Hi MyBucketList, have you tried https://www.airbnb.com/? It’s great for cheaper options around the bigger cities like Tokyo – there are options to stay book out an entire apartment or just a room with shared facilities, depending on your budget. I hope that helps!
Otherwise, if you google ‘ryokans’ in Tokyo, I’m sure you’re bound to find something there too – they’re basically a Japanese-style Inn.
Hope that helps!