Museums in Japan are very numerous and most of them are specialized in one precise domain: therefore each person can select the visits according to his/her interests.
Usually, museums are closed one day per week and for a few days during the New Year holiday period. Each institution chooses its entrance price; it can be free, from some symbolic Yens up to several hundred or thousand Yens. You can enjoy audio gears describing the museums in English or even more languages for the more touristy museums.
Be careful as during winter months, where the museums are the least attended, some may close their collections, even the permanent ones, to tidy up and clean up their departments before the new season, starting in April. Therefore, they remain opened but the visit might be limited to the outsides (buildings and gardens): it is advised to inform yourself before going.
The capital is home to the National Museum of Tokyo, the biggest and oldest museum of the country. Inside Ueno park, it presents a collection of more than 110,000 cultural and artistic works of Japan and Eastern countries, out of which some are categorized as National treasures or Important cultural Goods.
Art museums, whether they are dedicated to traditional arts or contemporary arts, can be found all across the archipelago. For example, the famous island of Naoshima is home to the Benesse Art Site, with several Modern Art buildings.
As a more surprising destination, we can find the typical exhibitions of the Edo Museum which recounts with numerous models the ancient popular life of Tokyo, or also the International Manga museum of Kyoto, enormous library dedicated to manga.
For those planning the discovery of several museums during their stay in Tokyo, the Grutt Pass booklet is to take into consideration. It is an annual package solution which guarantees the free or discounted entrance in some institutions. Available from April 1st to March 31st and then during 2 month from the date of activation, the Grutt Pass costs 2,200¥ (~US$21.25) per person. In 2018, it gave access to 92 places, including 83 museums in the Japanese capital.
A version of the pass for the Kansai region also exists. Costing 1,000¥ (~US$9.66) per person for 3 months, or 1,800¥ (~US$17.39) for 6 month validity, the Kansai Grutt Pass 2018 assures the access to about 50 museums, including in Kyoto and Osaka.
The purchase of these passes can be done directly in Japan, in the tourism information centers or offices.