In Tungufellsdalur (walley) there are several nice walking paths. There are all kinds of walking, through birch, in Svartárgljúfur the river Svartá runs through a small canyon and up on the hills Tröllbörn and Tófuhóll.
It is also possible to arrange a walk with the locals but you can ask for bookings on tungufell@tungufell.net
Icelandic version is here