One of our favorite places in Tokyo is Fujifilm Square at the Midtown complex in Roppongi. Every week or so there is a new photo exhibit on display, and there are often multiple exhibits at the same time. Entrance is free, and it is open to anyone.
There is typically a theme for each photo exhibit, whether it is based on activities, a certain photographer or group of photographers, domestic photos, overseas photos, certain places, vintage photographs, new photographs, etc.
If you are visiting Tokyo or live here and find yourself in Roppongi, it is worth taking a look.