Probably the most spectacular visitor attraction is the 16th century warship the Wasa. Housed in a purpose built building right next to Wasahamnen, the ship is something else. The Wasa is celebrated because it capsized on its maiden voyage, before it even got out of the harbour. Built basically too tall and thin, the ship was known to be tender, but all concerned passed the buck in celebrated style and blamed it on the king (who was away at the time). Spookily, no one was found guilty in the subsequent enquiry.... The ship was raised almost intact in the early 1960s and the exhibition, with both information and guided tours in English, is well worth a look. The sheer scale of the thing is breathtaking, and the building makes the most of vantage points to see the ship. The fascinating thing for me was to realise that the helmsman steered from below decks, and presumably couldn't see a damn thing.
Near the Wasa is the other big attraction, the open air museum, Skansen. A sort of look back over Swedish history, created at the turn of the century by another dedicated (mad) Swede, it has many original buildings and a small zoo. its generally refreshingly non-commercial, and the town square often hosts 'themed' days, where you can buy peasant food from people wearing native costume.
Nearby too, is the Tivoli, but this is a pale shadow of its namesake in Copenhagen.