You might want to spend some time browsing the exhibits at Bunker Museum, Kaliningrad Regional Museum of History and Arts, or Amber Museum. Ruins of Koenigsberg castle, Timber Bridge, and Brandenburg Gate are monuments to see when you're exploring the area around Cosmonaut Monument. You can watch performances at Kaliningrad Regional Drama Theatre, Kaliningrad Regional Philharmonic Hall, and Queen Louise Kirsch Puppet Theater if you're interested in local theater.