Stockholm is a city on archipelago, stands on 14 islands. There are so many tours but would cost you more but you can also experience natural beauty of archipelago on a cheap. Tours services usually starts from 250 SEK. . You may take ferries which would cost you from 50-150 SEK depending upon which island you wish to visit. 

Vaxholm is a town of archipelagos, you may find Waxholmsbolaget the most economic boat tour; would find ticket at half prices from October to March. It is wonderful experience to spend a day or two in the archipelago, It would take you closer to nature, Give you a Island hopping experience, Take you into the wild, And give you a feeling of being adventurous. 

If you are running short of time, and want to explore archipelago in just few hours, here are three places which you can visit in a very short time: 1-Gustavsberg and Värmdö 2-Fjäderholmarna 3-Vaxholm Find links on website main page to read more on Archipelago.