You might want to spend some time browsing the exhibits at Bunker Museum, B-413 Submarine Museum, or Amber Museum. Ruins of Koenigsberg castle, Honey Bridge, and Brandenburg Gate are monuments to see when you're exploring the area around Cosmonaut Monument. You can watch performances at Queen Louise Kirsch Puppet Theater, Kaliningrad Regional Drama Theatre, and Kaliningrad Regional Musical Theatre if you're interested in local theater.