You might want to spend some time browsing the exhibits at Art Gallery of the European and American Countries of the XIX-XX centuries, Pushkin Museum of Fine Arts, or Armoury Chamber. While you're exploring, swing by Cathedral of Christ the Savior, Grand Kremlin Palace, and Palace of Facets to learn a bit about the area. You can check out the local talent at Theater of Modern Drama, Moscow Arts Theatre, and Bolshoi Theatre.