We had both been to these countries before, though not together.
So, we picked a few things that we wanted to experience with each other

When you visit Stockholm, we would like to recommend that you visit
Gamla Stan, Ridderholmen, City Hall and the Vasa Museum before Skansen!
We enjoyed each of these places on our prior visits!
We loved Skansen, we spent about 4 hours there and would have liked another hour!

When you visit Oslo take a bus out to Holmenkollen - the site of the 1952 Olympic ski jumping competition.
There you will have dramatic views of Oslo Fjords. We would also suggest a visit to
City Hall and the National Museum and of course the 3 maritime museums ~
Viking, Fram and Kon Tiki

When you visit Copenhagen, we recommend the Copenhagen Card and the HOHO busses!
Do everything you can fit in that interests you ~ utilizing these 2 resources
Don't forget a trip to Tivoli For the best meal deal, buy a hot dog from the cart located
 in the Radhus Plaza grab a bench and enjoy the architecture

The muscic playing in Denmarks Album is the Prince of Denmarks March by Clark