Stockholm sits where Lake Mälaren meets the Baltic, and most of its best day trips involve getting out on the water. The archipelago alone runs to some 30,000 islands and skerries, easily reached by the Waxholmsbolaget ferries that fan out from the city centre.
The closest taste of island life is Vaxholm, an archipelago town about half an hour out by boat, with a 16th-century island fortress guarding the sea approach to the capital. Further south, Utö rewards the longer journey with sandy beaches, granite cliffs, old iron-mine shafts to explore, and a couple of good harbour-side restaurants — rent a bike and ride the island's quiet roads.
Inland, Mariefred makes a fine trip in the other direction, west across Lake Mälaren. Its main draw is Gripsholm Castle, a red-brick Renaissance fortress on the lakeshore housing the Swedish national portrait collection. In summer you can travel out on the coal-fired steamboat S/S Mariefred and return on the narrow-gauge heritage railway to Läggesta, where regular trains run back to Stockholm.