There are several animal cafés in Tokyo. Here are a few examples, besides these I saw mini pig, cat and there is also capybara cafės and probably others that I am not aware of.
I did not go to any animal cafės during my stay. And I love animals, therefore I didn't go. Would I like to hold a hedgehog, hug a capybara and pet an owl? Yes of course but I do not think it is right to hold these animals captive and allow a bunch of people to paw on them every day and take selfies with them over and over agaon. I am sure the animals are stressed.
If you really just have to go to an animal café.....look up ethical/guilt free animal cafés and go there. Do the right thing!