You'll want to browse the collections at Museum of Soviet Arcade Machines, Central Armed Forces Museum, and Dostoevsky Museum. Some landmarks that you won't want to miss include Ostankino Palace, Central Academic Theatre of the Russian Army, and Arch of the Main Entrance of VDNH. You can watch performances at Helikon-Opera, Theatre "No Signs", and Moscow State Historical and Ethnographic Theater if you're interested in local theater.