Tokyo has a wide selection of museums and galleries. Department stores often host temporary exhibitions, which are convenient and economical. Tickets can be bought on site, but there are often long lines for the more popular exhibits.
See also: the list of Museums and Art Galleries
Internet Museum is a museum search engine that stocks information on 7,800 museums in Japan (500 of them have information in English).
The Grutto Pass is of exceptional value at 2,000 Yen, giving you one-time admission or discount to 95* facilities, including museums, art museums, zoos/aquariums, and botanical gardens. The pass can be bought at any of the participating venues and is valid for 2 months starting from the first day of use. (*Subject to change. Check website for participating venues.)