Your first stop should be the historic Old Town of Gamla Stan and the Royal Palace. The Royal Guards perform a changing of the guard procession several times a week during summer, with reduced performances during winter.
Once you’ve wandered round the Old Town and bagged yourself some tourist paraphernalia, head north of the river to the trendy area of Ostermalm for some shopping. The area is a choice spot for going out at night.
The open-air museum of Skansen is worth a wander around. Founded in 1891 it’s also a zoological museum and is home to brown bears, reindeer and lynx.
In the afternoon head to Sodermalm and spend the afternoon relaxing in some of the many bars and restaurants that line the main strip of Gotgaten.