You'll want to browse the collections at New Tretyakov Gallery - Museum of Modern Art, Armoury Chamber, and Bunker-42 on Taganka. Sights like Cathedral of the Assumption, Cathedral of Christ the Savior, and Ivan the Great's Bell Tower are must-sees while exploring the area. You can watch performances at Glas Russian Spiritual Theatre, Moscow International House of Music, and Taganka Theatre if you're interested in local theater.