The Solheimasandur Plane Wreck is defintely a mysterious photo spot but there is nothing else to see there apart from the plane. The hike can take 2-3 hours one way and conditions can get very dangerous with high winds and sand storms and extreme cold. An alternative to the hike is paying an extra fee and taking the offroad bus that leaves every few minutes to the plane.
We visited for sunset here and there was no other soul around.