Never fear -- you will not be bored during your trip to Tokyo. The world's most densely populated city features everything from brightly-lit entertainment districts to quiet gardens. Though the city has excellent public transportation systems, we suggest you bring comfortable shoes and hit the streets. It's the best way to discover small temples tucked between modern office buildings, interesting shops, and sumos riding bicycles through their village. Whatever your interests, there are plenty of Tokyo attractions to explore.

1.Kabuki-za Theater
Tokyo’s signature performing art features amazing costumes, battle scenes, and stagecraft; melodramas of samurai and courtesans played by all-male performers; rent the English blow-by-blow audio narration.
2. New National Theater Tokyo
Opened in 1997; top venue for opera, ballet, and contemporary dance.
3. Noh
This hypnotic, sonorous theater art is the world’s oldest continuously in performance. Reminiscent of classical Greek theater; employs masks, grand robes, and great allegory.
4. Takarazuka Theater
All-female counterpart to the all-male Kabuki stage; presents revues and dramas; expect tuxes; English synopses available.
5. Tokyo Philharmonic Orchestra
Led by the Korean conductor Myung-Whun Chung; performs in venues including Suntory Hall and Tokyo Opera City (both worth a visit for their renowned acoustics).

I hope this helps :)

If you like history then the Edo Tokyo museum is great. It takes you through from the Meiji restoration through the industrial age so you can see how Tokyo evolved from the old days of Edo. There's lots of genuine artifacts as well as displays and dioramas to illustrate and help bring the past to life. At lunchtimes they often do special dance or culture displays as well. Well worth a visit! The museum is located right next to the sumo area in Ryogoku and there's a sumo museum in here (only small) which is free to enter - so you can do this one as well while you're there if you like. If you keep walking past the arena and go straight you'll come to a Japanese garden which is lovely to enjoy just walking round and escaping the streets for a few minutes.

For art museums then Ueno is fantastic! You can choose from Asian or Western art as there are different museums dedicated to each here. If you like science museums then head over to Odaiba. I like this area anyway as you get some great views of Rainbow Bridge and Tokyo Bay. You'll also find the Miraikan here - the future science museum - you can actively get involved with some of the exhibits as they require you to demonstrate how things work, you can clamber in an old space shuttle living room, or catch a show with the robot asimo. All good stuff!

Hope it helps!