In Shijuku area, or pretty much entire metropolitan Tokyo area you will have no problem finding public bathrooms.

As for cleanliness, it all depends on each personal preference and view. For me I have not encountered public bathrooms in Japan where I could not use it because of cleanliness. I have seen far worse public bathrooms in the U.S. However, I been with few people who mentioned that they rather not use specific bathroom due to cleanliness.

Western style toilet has become very common in public bathrooms in Japan, but still it is possible to encounter Japanese style toilet, the toilet in on the floor level and use by squatting.

I used to carry handkerchief or small hand size towel when in Japan, because pretty much most bathrooms in Japan have sinks with running water to wash hand but do not have paper towels to dry hands. However, these days I see air drying machine to dry hands in Japanese public bathrooms.

Talk about Japanese public bathrooms… I do not know about ladies rooms, but in men’s room in Japan I see far often that guys leave bathrooms without washing hands…

There is some benefit in keeping greeting by bow down rather than handshake in Japan…