In Copenhagen, we'll embark on a City and Harbor tour which mostly means we're ride a bus and canal boat and listen to a tour guide point out various sites along the way. We enjoy these types of excursions because they give a general overview of the city and there is still time in the day to do some shopping or exploring on your own - albeit with a mindful eye on the time.
The Little Mermaid statute is usually at rest in the harbor, but she is currently in Shanghai for EXPO 2010. When we were in St. Maarten in October, there is a half-sized replica of her at the port. We knew at that time that she would not be in Copenhagen, so we made sure to view her then. However, we've since learned that there is a live-feed video of her that stands in her place. ( http://www.usatoday.com/travel/destinations/2010-03-25-shanghai-little-mermaid-statue_N.htm ).
Our tour will also take us to Amalienborg Palace where the Queen of Denmark resides for portions of the year. ( http://www.frommers.com/destinations/copenhagen/A19466.html ). It is said to be the most beautiful square in all of Europe. We'll have to take pictures and post them for you to decide.