The Tokyo National Museum in Ueno Park is Japan's oldest and largest art museum, holding around 110,000 works spanning Japanese art from the prehistoric to the early modern period, plus collections of Asian art from China, Korea, and the wider region. The Honkan (Japanese Gallery) is the place to start — 24 rooms tracing Japanese art from Jomon pottery to Edo-period painting, including National Treasures that are shown on a rotating basis.
Budget half a day. The museum shop is excellent for high-quality reproductions and books. The surrounding Ueno Park clusters several other major museums including the National Museum of Western Art (a Le Corbusier building, UNESCO-listed) and the National Museum of Nature and Science.