The Royal Palace located in the center of Stockholm and is a must visit. The grand structure is impressive just to walk by but when you enter into the palace it is amazing to see how royalty lived with the grand rooms, intricate art and furniture, marble stairs and learn more about the history.
I also recommend getting a Stockholm Card if you want to see the main sites in the city. It is a great way to get discounts and get into places like The Royal Palace: http://www.visitstockholm.com/en/Stockholmcard/
Sure, you can pay your money and tour the royal palace in Stockholm but to me it was more interesting as the sun went down and the crowds disappeared. The only sounds that could be heard were the palace's guards marching back and forth in front of their posts. It is their responsibility to safeguard the palace. The cannons used to come in quite handy in the past as well.