You might want to spend some time browsing the exhibits at State Historical Museum, Armoury Chamber, or Moscow Museum of Modern Art. Explore notable local landmarks like Resurrection Gate, Bolshoi Theatre, and Kremlin Arsenal. You can watch performances at Stanislavski and Nemirovich-Danchenko Moscow Academic Music Theatre, A.R.T.O. Theater, and A.R.T.O. Moscow Theatre if you're interested in local theater.