You might want to spend some time browsing the exhibits at Central Armed Forces Museum, Gulag History Museum, or Moscow Museum of Modern Art. While you're exploring, swing by Central Academic Theatre of the Russian Army, Church of the Nativity of the Virgin in Putinki, 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, Moscow Theatre Et Cetera, and Tchaikovsky Concert Hall if you're interested in local theater.