There are only about 2 places, neither of which are close to Tokyo. One is in Nara Park. It has some of the best places to see in Japan. You can buy crackers to feed them, which they love. As for petting them, at best they'll tolerate it but not particularly like it.
The other place is on Miyajima Island in Hiroshima. Again, most shy away from you, but you may be able to gently pet a few who are sleepy or relaxing. My kid did it and enjoyed seeing them. But they are not like cats or dogs at all, just so you know.