I went to one in Tokyo and unfortunately it wasn't a very pleasant experience. The cafe itself was nice (though expensive) but the cats were so unsettled by so many different people going in all the time and so many other cats that it wasn't a good atmosphere. it might just have been that cafe but the cats were really stressed and unhappy.
I semi regularly went to a dog cafe when i was overseas and it was awesome...I dont like cats but was dragged to a cat cafe too and they were super chilled out. Cats not giving a damn like always, just swanning around like they owned the place...damn cats - -