What should I see on my European/Scandinavian "mini-vacation?"

[Piltdown13]

I'll be attending a conference in Sweden later this month, after which I've planned to stay on a week and do the tourist thing. I'll probably have about a day in Stockholm, and three days each in Berlin and Copenhagen.

So, for all DUers who have been to those cities -- What museums/attractions/etc. should I absolutely not miss? I'll have a rail pass, so will be able to do day-trip type stuff as well as the more centrally located attractions.

On the other hand, any sights not worth the bother?

I should probably note that I'm a woman and will probably be traveling alone (though, staying in hostels, you can never tell when you might meet up with a group to tag along with!).

Thanks so much, y'all!!!!

:-)