You'll want to browse the collections at State Historical Museum, Palace of Facets, and Cathedral of the Annunciation. 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 Bolshoi Theatre, Moscow Arts Theatre, and Stanislavski and Nemirovich-Danchenko Moscow Academic Music Theatre if you're interested in local theater.