You might want to spend some time browsing the exhibits at Bunker Museum, B-413 Submarine Museum, or Kaliningrad Regional Museum of History and Arts. Ruins of Koenigsberg castle, Amber Museum, and Honey Bridge are monuments to see when you're exploring the area around Cosmonaut Monument. You can watch performances at Kaliningrad Regional Musical Theatre, Queen Louise Kirsch Puppet Theater, and Kaliningrad Regional Drama Theatre if you're interested in local theater.