You might want to spend some time browsing the exhibits at State Historical Museum, Cathedral of the Annunciation, or Armoury Chamber. Moscow Arts Theatre, Kremlin Arsenal, and Bolshoi Theatre are some of the notable landmarks to see in the area. You can watch performances at Chekhov Art Theater, Moscow State Academic Chamber Music Theatre, and Stanislavski and Nemirovich-Danchenko Moscow Academic Music Theatre if you're interested in local theater.