You might want to spend some time browsing the exhibits at Museum of the Great Patriotic War, Battle of Borodino Panorama Museum, or Art4.ru Contemporary Art Museum. Triumphal Arch, V. Goryaev Museum, and VTB Arena are well-known local landmarks worth a visit. You can watch performances at Gypsy Theatre, Adrenaline Stadium, and Dramaturg Theater if you're interested in local theater.