There is a campsite at Þakgil and is located between Mýrdalsjökull (Mt. Katla) and Mýrdalssand. The name can be translated as "the canyon with a roof". The road to Þakgil is 14km from highway number 1 is one of the most beautiful "entrance" to a camp site that I've travelled to. The landscape is amazing around the road as well as further away. The camp site itself will be revealed at the last turn.