Our starting port. We arrived one day before the cruise started. I recommend the Canal & Harbor boat tour of the city. You board this boat at the end of Nyhavn and take the red line for the Harbor tour. You get your bearings from this trip. Also, go inside Tivoli...especially at night. We were apprehensive of spending 95 krone, but it was well worth it to give you a view of Danish culture and people. Don't waste your time (or money) with the tourist Ice Bar or Cafe Europa on the Stroget. We traveled by pedicab from the boat tour at Nyhavn to Tivoli for $20US and had a wonderful tour. We spend the night at the Hotel 27. Do not stay here...it is next to a few bars and if you want noise all night long, this is your place. Also, the hardware floor was filthy. The cab ride from the airport to the city center was expensive...130 krone.
I'm including Oslo here. You really don't need to spend $$$ on a tour. There's not much to see in the city of Oslo. Some passengers went to Vigland and they were disappointed. Shuttle buses to City Center (City Hall) available.