You might want to spend some time browsing the exhibits at Glinka National Museum Consortium of Musical Culture, A. N. Scriabin House Museum, or Gulag History Museum. Sights like Yeliseyev Grocery Store, Stanislavski and Nemirovich-Danchenko Moscow Academic Music Theatre, and Moscow Arts Theatre are must-sees while exploring the area. You can watch performances at Tchaikovsky Concert Hall, Hermitage Moscow Theater, and Chekhov Art Theater if you're interested in local theater.