Several people has already mentioned Finland (and I haven't been there, have only been recommended places), so I'll stick to Norway and Sweden.
Norway will be expensive, doesn't matter if you're in the capital or other cities. Buy yeah. Deal with it :P In the capital itself you have several sights, famous parks (ie. Vigelandsparken - heaps of quirky statues, it's the largest sculpture park made by one single artist in the world), the castle, the fortress etc.
It's fjords, cities with northern lights and midnight sun, glaciers, mountain or sea side experiences, all depending on the likes and dislikes. Depending on the time of the year, there's a lot of festivals. A lot of this will also be the same for Sweden, since there's much of the same climate. Not as much fjords, though.
As there's been Swedish nobles for centuries, there's also loads of mansions, castles, fortresses and churches built in the honor of nobles, kings and what-not. Loads to see!
Source(s):
http://www.visitfinland.fi
http://www.visitsweden.com/
http://www.visitnorway.com/
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