Offshore there are over 24,000 islands to explore and many Swedes have boats in local marinas so that when summer comes to the city they can set off and explore the multitude of islands that dot the Baltic with green. Some are tiny, others have homes and are inhabited by Swedes who want to escape from the city. Some even row into the city each day for work.
If you want to spend some time in and around the islands, several boat companies offer day and half day tours. Within the city itself, others offer different tours of the waterways and islands and seeing the city from the water is a great way to be introduced to its charms. You can combine the water tours with city bus tours with guides that will explain what you are seeing. Do a tour and then return later to the ones you find most interesting.