Bijutsukan (美術館) means art museum. The word matters when reading Tokyo listings because it draws a line the English word "museum" blurs: 美術館 is for art, while hakubutsukan (博物館) covers history, science and natural history. The Tokyo National Museum is 博物館; the National Museum of Western Art is 美術館.
You'll see the suffix on almost every major venue — 森美術館 (Mori Art Museum), 東京都現代美術館 (Museum of Contemporary Art Tokyo), 国立西洋美術館 (National Museum of Western Art), SOMPO美術館. A venue named ギャラリー (gallery) is usually smaller, and often free.
Two practical habits: most bijutsukan close on Mondays (or the following weekday when Monday is a public holiday), and most stop admission 30 minutes before closing.
See also kikakuten and shozohin-ten, or browse exhibitions in Roppongi.