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Even if museums are not your thing, Moscow has some amazing options, including The State Tretyakov Gallery (which houses only Russian art); the Pushkin Museum (for more international collections); and the Kremlin Armory Museum for a look into some unique items, such as the ivory throne of Ivan the Terrible and gold-covered imperial carriages. The Bolshoi Theater, one of the largest ballet and opera theaters in the world, is also worth a visit if you can get tickets. 

Some of the best things in Moscow require some walking to be properly explored, such as the pedestrian-only shopping street Stary Arbat and the boardwalk along the River Moskva.