Elliðaárdalur
A 15-minute bus ride from central Reykjavík lies Elliðaárdalur Valley, a large green, public space. It's a very popular destination with the locals for all sorts of outdoor activities, including jogging, biking, walking, horseback riding, fishing, and playing.
Through the valley one of Iceland's best salmon-fishing rivers. Fishing is not allowed for everyone, to get a permit one will have to join Reykjavík's Fly-fishing Club and partake in an annual lottery. However, everybody is welcome to navigate the banks of the river, and perhaps see a hunter skillfully catch a salmon.