You might want to spend some time browsing the exhibits at Central Armed Forces Museum, Vasnetsov House Museum, or Gulag History Museum. While you're exploring, swing by Central Academic Theatre of the Russian Army, Stanislavski and Nemirovich-Danchenko Moscow Academic Music Theatre, and Starye Polya to learn a bit about the area. You can watch performances at Obraztsov Puppet Theatre, Bogis Theatrical Agency, and State Theater of Nations if you're interested in local theater.