For a nice afternoon walk, the perfect address is Kunglige Djurgården (Swedish for “The royal animal garden”). It offers a variety of trails, of which some are by the water and some are through the forest. It is also connected to Rosendals Trädgård, which offers a café and gardening articles. There are usually a lot of people, but the forests behind the garden are usually peaceful and quiet. You might even stumble across some deer or a woodpecker.
How to get there: From Slussen, get the ferry number 82 to Djurgården. From the terminal Almänna gränd it's a 1.5 kilometre walk to the park. Alternatively, you can also take the above-ground train 7 from T-Centralen to Djurgårdsskolan.