You might want to spend some time browsing the exhibits at Amber Museum, Bunker Museum, or Kaliningrad Regional Museum of History and Arts. Ruins of Koenigsberg castle, King's Gate, and Honey Bridge are monuments to see when you're exploring the area around Wrangel Tower. You can watch performances at Kaliningrad Regional Drama Theatre, Kaliningrad Regional Youth Theater for Young Spectators, and Queen Louise Kirsch Puppet Theater if you're interested in local theater.