Not like in Europe, probably not so many foreigners will visit the theaters in Japan. Opera, musical and ballet are not played everywhere daily. Then these cultural performances are much more for limited people, who are keen on these performances.
Play, drama played at the theaters are much more frequent than operas but you can watch at big cities only. Then, the interesting thing is that these plays are able to be watched during the day, hard to find the performance which starts in the evening.
For example, I have watched a play in Fukuoka at Hakataza theater due to one of the actresses is my friend but the performance started at 11:00 in the morning of a Tuesday! Therefore as you can imagine, the performances are mostly targeting elder Japanese who has much time during the day. If the play starts at 14:00, it will finish around 17:00 and you have to rush home to make the supper. If the play finishes at 14:00, you can have a tea with your friend or enjoy shopping before reaching home and make a supper.
By the way, theater ticket system is not as same as in Europe and no e-ticket is available. Therefore if you want to visit the theater during your visit in Japan, you might need someone to get the paper ticket. Then, the another difference is that there are many shops inside the theater where you can buy not only refreshments but also proper meals and souvenirs.