You might want to spend some time browsing the exhibits at State Historical Museum, Cathedral of the Annunciation, or State Museum of V.V. Mayakovsky. Some landmarks that you won't want to miss include Palace of the Romanov Boyars, Spasskaya Tower, and Moscow Kremlin. You can watch performances at Maly Theatre, Bolshoi Theatre, and Chekhov Art Theater if you're interested in local theater.