If you want to find cats in Japan, you would have the best luck by going to shrines and temples. Why?
There are two reasons:
One is that the shrine and temple grounds are “public” places where nobody stops you to come in, even if you are a cat. In fact, they used to be the only public places in Japan. The notion of a public park was imported from Europe/America in late 19C . Many community gatherings still take place there, so why not cats’ gatherings?
The other, probably more important, reason is that architecture and landcape of shrines and temples offer comfort and safety to cats. Their buildings always have decks (:enn) with deep eves over them. On the decks, cats can sun-bath on fine days and have naps on rainy days without gettint wet. A space under the deck can come in handy for them, too. If you are chased by big dogs or nasty boys, that is where you would run into.
And do not forget trees and shrubs! Japanese shrines and temples tend not to have ridgid fences. Instead, they have woods as loose boundaries. Cats can hunt and hide as they wish in that sacred forest.
Next time you visit Japan, please try visiting one of shrine/temple grounds. You will be rewarded by a cat meditating on enn. (Y)