What we did was visiting Drottningholm, inside and the garden behind it. We also tried to find Hagapark. I want to emphasize the word "tried" because after leaving the metro at the right station according to the map, we walked half an hour in all directions and since there was no park, we just skipped it and want to try it again the next time we're in Stockholm.
Sunday morning we went to see the lysning, banns of marriage, of Princess Madeleine and Chris O'Neill at the Royal Chapel inside the Royal Palace. I was seated more in the back of the church, so I just got a glimpse of the Royal Family and only saw their faces.
On the plane back we decided that it's time for Copenhagen next year :)