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