This canyon, probably formed at the end of the last Ice Age, is definitely worth the trip. Today, it is roughly 2 km long and up to 100 m deep. Make sure to admire the scenic views as you hike along the Fjaðrá river. You can also follow a more relaxed path along the canyon's edge, looking down at the mesmerising natural beauty. The best season to visit is summer, because once the canyon is hidden under snow, the paths often get inaccessible.
Fjaðrárgljúfur is located near the village of Klaustur, about 300 kilometres from Reykjavík. If the weather conditions are bad, the road to the parking lot might be closed. It's doable even with a normal car, but 4x4 is definitely better for this particular place.
Coordinates 63°46'21.358" N -18°10'25.397" E