You'll want to browse the collections at New Tretyakov Gallery - Museum of Modern Art, Art Gallery of the European and American Countries of the XIX-XX centuries, and Gallery of 19th and 20th Century European and American Art. While you're exploring, swing by Cathedral of Christ the Savior, Armoury Chamber, and Cathedral of the Assumption to learn a bit about the area. You can watch performances at Forum Hall, Moscow International House of Music, and Taganka Theatre if you're interested in local theater.