You'll want to browse the collections at New Tretyakov Gallery - Museum of Modern Art, Pushkin Museum of Fine Arts, and Museum of History of Moscow. Cathedral of Christ the Savior, Armoury Chamber, and Grand Kremlin Palace are notable landmarks to explore if you're in the area. You can watch performances at Anton Chehov's Theater, Moscow Arts Theatre, and Chekhov Art Theater if you're interested in local theater.