A modern, large, impeccable facility to watch Opera, Classic, Theatre and Musicals. They show quite varied repertory of spectacles and plays. Even if you do not understand japanese, there are musical concerts that may suit your taste. They also have a lot of japanese interpretation of foreign plays. If you want for some underground, experimental theatre, I will go to Shimokitazawa.

To access here, take the train until Hatsudai Station of Keio line, or it is a 15min taxi drive from Shinjuku station if you can afford it, since taxis are a bit expensive. There is also a restaurant on the 53th floor if you feel like it (but I would go instead for a small restaurant in the nearby Hatsudai commercial street).