The only place I know in the whole country is the Zao Fox Village in Miyagi. There was another place I visited in Hokkaido about 30 years ago, but I don't even know if they are still there. Nevertheless, at the Zao Fox Village, you are not allowed to touch the foxes - they are not pets and they can bite. The other big issue is poor transportation options - renting a car to drive there is the most convenient and useful. Your second choice is a morning bus, but you must be staying the night before close by to get it - going up from Tokyo in the very early morning is simply impossible. Your last choice is a taxi - which takes close to an hour and costs around 10,000 yen each way - not smart. In Tokyo, there are of course many cat cafes, owl cafes and others. I enjoyed going to the Machida Squirrel Park in my last visit - I got 200 instant friends the moment they saw I had food, and they were climbing up my legs up to my shoulders. You really couldn't pet them either, but it was quite an experience.