If you have spent a few hours at Gamla Stan, and want to go to Djurgården, you should take the Djurgården ferry.
As Stockholm is made up of 14 islands, one of the best ways to get around is by boat. We boarded a boat at the Royal Palace and went off to Djurgarden. Then from there we went by boat to Sondermalm.
To get a good impression of Stockholm: get into a boat. At the palace at Gamla Stan you can do boat tours. One hour tours cost only 8 euros per person.