One of the places you definitely have to visit when in Stockholm is Skansen, the world's oldest openair museum. It is written in every guide, and with a reason. It tells you about swedish history, lets you see moose and provides a beautiful view over the city. Skansen is on the island of Djurgården, the museum island. There are two entrances, the main one at tramstation "Skansen", where there is an escalator to the mainpart, or the smaller one, Hazelius, close to the Nordiska museet, where you can either walk up or take the bergbana for a small additional fee.
Once up, you're free to discover the museum that takes you back through swedish history, how life was in earlier centuries and in the different regions of Sweden. There are many houses with original interior from that time and people doing handscraft while explaining it to the visitors. You're free to ask questions anytime, everybody speaks perfect english and many also other languages. See how glass is made, how chairs were repaired, how letterpress worked, how the delicious kanelbullar are made (be prepared for lining up, but it is worth it), discover old postoffices or huts of the Sami people of Lapland , the wooden church Seglora kyrka and many other interesting buildings and places.
And there are many animals, especially nordic ones. So depending on when you visit, you can see moose, peacocks, reindeers, owls, bisons and many more. And there are also many places where you have a beautiful view over Stockholm. And, depending on the time of the year, there are also markets or the celebration of midsummer. Take your creditcard, as on most places, you cannot pay cash. Calculate at least half a day there to visit everything.
Find all the information about the opening hours, entrance fee, activities and events on the official website.