If you're looking to get a bit of the beaten path you've come to the right place. No where else in Iceland have I experienced as much desolation as in the valley of Kjos. While the area around the Skaftafell info center is swarming with tourists, in this hike, I didn't see a single soul (human, that is, sheep-souls were plenty). During this hike you'll make your way through a glacial valley. You'll be able to spot the glacial tongue in the distance. Around you strangely formed mountain cliffs rise up steeply.
About the trail
Start your hike at the Skaftafell camping. The national park requires an entry fee that will be waived if you stay at the camping. If you're into hiking it is totally worth staying a few days, as there are plenty of paths to explore. The national park has a reception. I found the staff to be very helpful. They provided me with a map and can advice you about the weather conditions in the mountains.
This hike might not be challenging altitude-wise, but it makes up for it in sheer distance and rough terrain. Make sure you are prepared for this challenge.
You'll deal with most of the height meters right at the start as you'll go up and over a small mountain ridge. A bit further a bridge takes you over a glaciel river into the valley. You'll follow the path that crosses the valley to it's western side. Here, the path continues through birch forest, sheep are grazing in this area. The path goes in and out of the birch forest. When not walking through the forest you'll hike through rocky terrain in the valley. There are yellow markings along the trail, but they're not consistently present.
After a while the valley opens up to the left, this marks your entry to the valley of Kjos. You'll see impressive cliffs to the north and south. Your goal is a small waterfall at the end of the valley. As you make your way over the rocky terrain an actual path might be hard to find. The river coming down in this valley meanders in a dozen smaller rivers and it will be hard to avoid hiking crossing them. As they are quite small I wouldn't call these crossings risky. It is propably not worth taking your shoes off as there are so many. It's best to accept that you'll continue your walk with wet feet. A pair of merino wool hiking socks can help keeping your feet warm here.
Where the valley becomes very steep and the river comes bouldering down at a high speed it's time to turn back. You'll take the same route back as you came untill you reach the part where you crossed the valley. Here you'll follow the path further north and cross the valley soon after. You continue on until you reach the camping.