You might want to spend some time browsing the exhibits at State Historical Museum, Palace of Facets, or Cathedral of the Annunciation. Sights like Spasskaya Tower, Moscow Kremlin, and Ivan the Great's Bell Tower are must-sees while exploring the area. 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.