In the 27-story building erected as part of the Kabuki-za remodel completed in 2013, you will find a small museum dedicated to kabuki. It is filled with memorabilia such as props and costumes from past shows. Though none of the signage is in English, it is interesting to see the colorful items up close, especially if you pair a visit to the museum with one to see a performance at the theater next door.
The museum is on the 5th floor of the Kabuki-za Tower, easily reached from the Tokyo Metro Higashi Ginza Station. It costs 500 yen to enter, and is open from 10 am to 4 pm.
Kabuki-za Museum (photo: tenugui/flickr)
Website is only in Japanese but has some great pictures to give a sense of what your enjoyments of the history of Kabuki-za: http://www.kabuki-za.co.jp/siryo/
