Best, or most popular cat cafe in Tokyo? Thank you in advance.

I don't know how you define "best', but you can choose what appeals to you most from a good list here. Of course timing matters as well. Cats sleep most of the day (like afternoons), and if you are in a crowded place then the cats may get overstimulated and not want the attention. If you want a more natural experience, you could also go to Enoshima, which is one of Japan's "Cat Islands"

Thank you....cat cafe calico seems to fit the bill!