You might want to spend some time browsing the exhibits at Vasnetsov House Museum, Central Armed Forces 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 Bolshoi Theatre 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.