The Kjölurvegur trek is an excellent two- to three-day hike from Hveravellir to the glacial lake of Hvítárvatn, following the original Kjölur route that ran west of the present Route 35, hugging the slopes of Langjökull: it’s punctuated by overnight huts run by Ferðafélag Íslands (book in advance through), roughly four to six hours’ walk apart.
From the springs, follow the F735 west towards the glacier for roughly 14km to the Þjófadalir overnight hut. Here the jeep track peters out into a walking path as it swings southeast, around the tiny Hrútfell glacier, to another overnight hut at Þverbrekknamúli. From here, it’s a further straightforward hike of around four to six hours to reach the Hvítárnes hut, an idyllic if somewhat lonely place to break the journey – the hut is supposedly haunted by a young woman who lived hereabouts when the area was farmed, though only men who sleep in a certain bed in the hut will see her.
From the hut, it’s an easy 8km walk back to Route 35 and the bus to either Reykjavík or Akureyri, passing the beautiful Hvítárvatn glacial lake, at the foot of Langjökull, on the way.