The best way to experience a city is by walking!
Start by taking Djurgårdsfärjan, the ferry-boat, from Slussen. It goes every 15 or 20 minute. If you have a subway card you get on for free! Don’t forget to tell them that you’re jumping off at Skeppsholmen. If you forget you’ll end up at Djurgården, which is a beautiful island as well, so no worries!
In addition to beautiful views you can also visit interesting spots like the Museum of Modern Art, the Architectural Museum, the East-Asian Museum, theatre Galeasen & Af Chapman, which is a youth hostel on water. Also, in the small park which is situated in the middle of everything, you can enjoy Niki De Saint Phalle‘s and JeanTinguely‘s sculptures from 1966.