You might want to spend some time browsing the exhibits at State Historical Museum, Cathedral of the Annunciation or Armoury Chamber. While you're exploring, swing by Bolshoi Theatre, Kremlin Arsenal and Moscow Kremlin to learn a bit about the area. You can check out the local talent at Stanislavski and Nemirovich-Danchenko Moscow Academic Music Theatre, A.R.T.O. Theater and A.R.T.O. Moscow Theatre.