I love to go to Fjhäderholmen during summer! Its probably the closest located Archipelago trip from the city that you can do. Its a really great location for a day trip, but make sure to plan a whole day for this. There are several operators that will take you to the island and boats leave frequently to and from the island. There are lots of restaurants and bars on the island and also some craft shops & boutiques. You can also join the Stockholmers on the cliffs to tan and swim.

good to know: you can only use the boats of the operator you bought tickets from.