You might want to spend some time browsing the exhibits at State Historical Museum, Cathedral of the Annunciation or Nemirovich-Danchenko's Apartment Museum. While you're exploring, swing by Bolshoi Theatre, Resurrection Gate and Lenin's Mausoleum to learn a bit about the area. You can check out the local talent at Maly Theatre, Moscow Arts Theatre and Stanislavski and Nemirovich-Danchenko Moscow Academic Music Theatre.