You'll want to browse the collections at State Historical Museum, Cathedral of the Annunciation, and Armoury Chamber. Lenin's Mausoleum, Spasskaya Tower, and Resurrection Gate 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.