You cannot miss Kungliga slottet, the royal palace, when in Stockholm. It's visible from far away. Have you ever wondered how the official residence of the swedish king looks like inside? It can be visited all year around. You can buy a ticket for SEK 180 and within seven days, you can visit the Royal palace, Tre Kronor Museum and the Treasury. For SEK 30 extra, there is a guided tour. There are several guided tours per day in english and depending on the time of year also in many other languages. I would really recommend you to do a guided tour, as there are many interesting infos about Sweden's history, the story of swedish royality and also explanations about the - sometimes breathtaking - rooms you visit.
Get all the information about opening hours, guided tours, fees and group visits on the official page of the royal palace.