Sweden's capital and an amazing little city, Stockholm is situated on several islands in the Stockholm archipelago. I stayed at the hostel Af Chapman, run by HI, which has two parts: lodging on a renovated ship or within the HI building. I highly recommend the ship for those who have always dreamed of the seafaring life. Let me tell you, it's not pleasant all the time, but is well worth it, in my opinion.
For things to see in Stockholm, I really can't say specifically. I did a multitude of things which I came upon by exploring. Gamla Stan is the 'old town' of Stockholm. North of Skeppsholmen island (where Af Chapman hostel is), you reach a very pretty garden area. Nearby are banks so you can withdraw from ATMs. As you walk beside the harbour, you can't miss the multitude of ferries. Ask the captains, or get a timebook, and hop on one to get out to the archipelago. Farther north is the huge commercial district of Stockholm (the name alludes at the moment). It's quite immense, and you can't miss it.
Walking around the island of the Skeppsholmen bridge to the right will bring you to a marine where you can rent out a motorboat (it's quite expensive) or a sailboat (there's no way you'll get it out into the wind from this location). If you have been a good budget traveler (been under budget), and it's a nice day, rent the motorboat and split the costs with another person (hmm...picnic with a hot Swede maybe?).
One day, take a ferry out to the archipelago. One of the closest islands is Vaxholm. From there, you can ask the tourist office the location of a nearby kayaking place (it's on another island) and catch the bus there (might cost money, might not depending on the kindness of the driver). Anyway, the place rents out kayaks and some other sporting equipment (tents and such). Rent a kayak and head out into the archipelago. This is a wonderful way to while away a day.
Af Chapman
ph: 463 2266
email: info@chapman.stfturist.se