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 Timber 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 Musical Theatre, and Kaliningrad Regional Youth Theater for Young Spectators if you're interested in local theater.