You'll want to browse the collections at Bakhrushin Theatre Museum, New Tretyakov Gallery - Museum of Modern Art, and Cathedral of the Annunciation. Sights like Armoury Chamber, Cathedral of the Assumption, and Cathedral of Christ the Savior are must-sees while exploring the area. You can watch performances at Moscow International House of Music, Taganka Theatre, and Theater of Modern Drama if you're interested in local theater.