You might want to spend some time browsing the exhibits at Amber Museum, B-413 Submarine Museum, or Bunker Museum. King's Gate, Timber Bridge, and Brandenburg Gate are monuments to see when you're exploring the area around Wrangel Tower. You can watch performances at Kaliningrad Regional Philharmonic Hall, Art House Concert and Theater Complex, and Kaliningrad Regional Youth Theater for Young Spectators if you're interested in local theater.