Top places to see:

Old town
The Old Town or Gamla Stan consists of medieval alleyways, cobbled streets, and archaic architecture, as well as the islands of Stadsholmen, Helgeandsholmen, Strömsborg, and Riddarholmen.

Moderna Museet
The place to see Swedish and international modern and contemporary art.
www.modernamuseet.se | Skeppsholmen, 10327 Stockholm

The Archipelago
Magnificent collection of over 30,000 islands, islets and skerries only 2 hours away from Stockholm by boat or by car.

Skansen
First open air museum and zoo in Sweden on the island of Djurgården.
www.skansen.se | Djurg, Stockholm

Millesgården
Carl Milles is one of Sweden's most famous sculptors, and Millesgården was Carl and Olga Milles' home on the island of Lidingö. Now it is an art gallery that exhibits modern and contemporary art, including a sculpture park that provides a beautiful view over Stockholm and the harbour entrance.
www.millesgarden.se | Herserudsvägen 32 Lidingö, 181 34 Stockholm