I'm happy to report that Tokyo has been getting a better vegan scene in the recent year. When I moved to Tokyo 3 years ago, I couldn't find too many places but recently, I have seen many vegan or vegetarian restaurants around the city.
I'm actually a pescetarian but I would say 85% of the time I eat vegetarian on a regular basis. I've only been to a few vegan restaurants but here are my 2 favorites so far.
Restaurant 8ablish in Omotesando
A sister restaurant with Pure Cafe, Restaurant 8ablish offers Mediterranean style vegan food not commonly found in Japan. I ordered Souvlaki Plate and ended with soymilk ice cream (with bergamot oil) and couldn't be happier!
T's Restaurant in Jiyugaoka
Located in Luz Jiyugaoka, this place has friendly staff and offers Japanese, Western and Chinese vegan food that were all really delicious. I especially like their curry set with soy meat.
Also, Happy Cow is a really good vegan restaurant guide site that I swear by. I've been searching for a lot of vegan restaurants in Tokyo but they have lists for cities all over the globe!