Maybe it was just a matter of the time of day we were there, but "Time for Cats" seems like one of the sleepiest cat cafes we've ever visited. Main activities here seem to be a) napping, and b) scouting out locations for upcoming naps. There was a flurry of activity when one cat drank some water, but that was about it - overall it was a very relaxing experience, and we began to feel a bit sleepy ourselves.
Fortunately our admission fee included a cup of coffee at the adjacent cafe, called Holy Land, which is equipped with windows looking onto the cat playroom. Holy Land often has a friendly dog in residence, and they're open well into the evening, when they serve wine (Chilean wine Gato Negro) and a light cafe food menu.
In operation since March 2004, Time for Cats claims to be Japan's oldest cat cafe and currently has eighteen resident felines. Among the exotic breeds are a Burmese, a Japanese Bobtail, and a cross between an American Shorthair and a Bengal, as well as many Munchkins, Ragdolls, and Shorthairs. The website has a rather poignant photo page of "gone but not forgotten" previous residents.