You might want to spend some time browsing the exhibits at Amber Museum, Bunker Museum, or B-413 Submarine Museum. 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 Queen Louise Kirsch Puppet Theater, Music theatre on Basseynaya, and Kaliningrad Regional Musical Theatre if you're interested in local theater.