You might want to spend some time browsing the exhibits at Metro Museum, Garage Museum of Contemporary Art, or New Tretyakov Gallery - Museum of Modern Art. Novodevichy Convent, I.S. Turgenev Museum, and Cathedral of Christ the Savior are monuments to see when you're exploring the area around Gagarinsky. You can watch performances at Great Moscow Circus, Moscow International House of Music, and The Cherry Orchard Theater if you're interested in local theater.