You'll want to browse the collections at State Historical Museum, Palace of Facets, and Cathedral of the Annunciation. Spasskaya Tower, Resurrection Gate, and Moscow Kremlin are monuments to see when you're exploring the area around Red Square. You can watch performances at Maly Theatre, Bolshoi Theatre, and Stanislavski and Nemirovich-Danchenko Moscow Academic Music Theatre if you're interested in local theater.