Hi, Ginny,
If I recall, the city center is about 1/2 an hour from the airport. I like to allow at least 3 hrs prior to an international flight. Copenhagen didn't have the security bottlenecks that one encounters at LAX.
Not sure if you can leave your luggage with the ship. When we disembarked, the Voyager left that evening for another cruise. Maybe others have a answer for the luggage dilemma.
Still recommend the Hop on Hop Off bus for a general overview of the City. See the crown jewels (nothing like you will see in Moscow or London) but gorgeous nonetheless. I gave my husband several suggestions for Christmas and he surprised me with a lovely photo of the jewels. Oh well, I keep trying....... :D
The Little Mermaid is right by the ship & the bus makes a stop there too. Take a canal cruise - gives you a different perspective of the city and has some great low bridges - just don't stand up! :eek: Stop by Tivoli if time permits.
Have fun!
Miriam