You might want to spend some time browsing the exhibits at Matryoshka Museum, Moscow Museum of Modern Art, or Gulag History Museum. Sights like Alexander Goldenweiser's Memorial Flat Museum, Stanislavski and Nemirovich-Danchenko Moscow Academic Music Theatre, and Bolshoi Theatre are must-sees while exploring the area. You can watch performances at Theater of Modern Drama, Anton Chehov's Theater, and The Cherry Orchard Theater if you're interested in local theater.