You might want to spend some time browsing the exhibits at Gulag History Museum, Dostoevsky Museum, or Museum of Decorative & Folk Art. While you're exploring, swing by Central Academic Theatre of the Russian Army, Lenkom Theatre, and Stanislavski and Nemirovich-Danchenko Moscow Academic Music Theatre to learn a bit about the area. You can watch performances at Moscow Durov Animal Theatre, Bolshoi Theatre, and Maly Theatre if you're interested in local theater.