In your opinion, what would be the best city in Scandinavia to visit during Christmas and New Year's?
IMO the best city in Scandinavia is Copenhagen, most to see and do. If I'm picking one city, that's it.
"Best" will depend on your interests. If cross country skiing gets a lot of points in your equation, Oslo combines a city experience with cross country skiing a tram ride away.
http://www.visitoslo.com/en/your-oslo/winter/cross-country-skiing/
That said, early December is still Fall and snow in Oslo will not be as reliable as more northerly higher elevation venues which takes you away from your "city" requirement. http://www.oslo.com/v/geography/
Copenhagen for me, too! It's got such a huggly snuggly merry twinkly vibe going on that you cannot fail to be cheery and Christmasy bright! Lots of stuff to do, great food, friendly people - and at Christmas, all that seems to be on steroids.