I did the Century twice to the Baltic. My itinerary didn't include Berlin. For St Petersburg I did the 2day tour through this
In Copenhagen I walked from the ship along the harbor all the way to the Pedestrian mall. You can walk the mall all the way to the end to Tivoli. There is lots of shopping and museums to see. With your Dad you may want to take a taxi. In Stockholm you can take a taxi over to Old Town and go to the Palace and watch the changing of the guards. In Helsinki you can catch a ferry ride in the harbor and get a historical tour of the area. All three cities have hop on/off busses.