From Stockholm's City Hall quays you can catch a steam ship to Drottningholm with several departures in each direction (April to October) so it is easy to get back too. It is a very scenic and relaxing journey and in fact commuters on the Mälaren islands sometimes do it summertime so they can enjoy reading the morning paper on deck.
Well, not by the commuters who go to Stockholm City every morning, but you will see that most of them live in the communities closer to Stockholm and once you get further out, it is easier to discover by car. Nevertheless, getting to Ekerö and the Mälaren islands are still easy, after all they belong to the capital's public transport. If you come from Stockholm, take the underground to Brommaplan (the green line towards Hässelby for instance) and then one of the many buses to different islands. Summertime, you can also go by boat from Stockholm City Hall.