dwlt will be in Uppsala/Stockholm this weekend. Here is a short list of suggestions of things to do.
Uppsala: visit the cathedral (Domkyrkan). The town itself is a very nice place, Sweden's Oxford.
Stockholm: the Vasa Museum is well worth a visit.
The museum is on Djurgården, a park to the east of the centre of town. Waldermarsudde is an art gallery at the other end, with a very nice walk in between. Fans of Edvard Munch and Nietzsche will enjoy Thielska Galleriet in the same general area.
Visit the Stockholm Archipelago with a trip on the Vaxholm boats. Many different destinations for different timescales.
Stockholm Old Town, Gamla stan, in the middle of the city. The Royal Palace is here. South of the Old Town is Söder, literally South, the more Bohemian of Stockholms neighborhoods. Lots of bars, galleries, parks...
Eat traditional, if expensive Swedish food at KB or even more expensive seafood at Wedholms Fisk.