You might want to spend some time browsing the exhibits at War of 1812 Museum, State Historical Museum or Cathedral of the Annunciation. While you're exploring, swing by Bolshoi Theatre, Resurrection Gate and Lenin's Mausoleum to learn a bit about the area. You can check out the local talent at Moscow Arts Theatre, Stanislavski and Nemirovich-Danchenko Moscow Academic Music Theatre and Lenkom Theatre.