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 Alexander Goldenweiser's Memorial Flat Museum to learn a bit about the area. You can watch performances at A.R.T.O. Theater, A.R.T.O. Moscow Theatre, and Bolshoi Theatre if you're interested in local theater.