I spent a couple of nights in Stockholm just a few days before the shortest day - so it didn't get light until about 8am, and the sun was setting by 2pm. Quite depressing really, but the Swedish have a tradition of lighting candles, to cheer their spirits - so the centre of Stockholm had candles everywhere!
If you're into museums then Stockholm is the place for you - there are over 70 of them in Stockholm City! The best has to be the Vasa Museum - the Vasa was a Swedish war ship that capsized in Stockholm harbour on it maiden voyage - it was raised (in one piece) back in the 60's. It's amazing how much of the ship survived - it has to be seen to be believed.
If you get the chance it's also worth having a look at the Ice Bar - in the Nordic Sea hotel. The whole place is made out of ice, even the drink glasses. The place is kept at -6C. They do charge entrance - but you get a drink as part of that.
It's worth thinking about getting a "Stockholm Card" from the tourist office - it gives you access to a number of museums, and local transport - if you plan to visit a few museums, then the card is well worth it.