Formerly the Museum of the History of Moscow, this excellent museum has a new name, a new location and a new mission. The permanent history exhibit demonstrates how the city has spread from its starting point at the Kremlin. It is heavy on artefacts from the 13th and 14th centuries, especially household items and weapons. More exciting, the museum has space to launch thought-provoking temporary exhibits, including artists' and other local perspectives on the city.
It's housed in the former warehouses and garages of the Defense Ministry, with a central courtyard that displays outdoor art and interactive exhibits.