You might want to spend some time browsing the exhibits at Central Armed Forces Museum, Gulag History Museum, or Glinka National Museum Consortium of Musical Culture. 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, Obraztsov Puppet Theatre, and Sphere Moscow Drama Theater if you're interested in local theater.