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, Cathedral of Christ the Savior, and Pushkin House Museum on Arbat are monuments to see when you're exploring the area around Gagarinsky. You can watch performances at Great Moscow Circus, Forum Hall, and Moscow International House of Music if you're interested in local theater.