Here you can find literally everything what you are looking for in a campsite. Lot of space for tents, campers, cabins, well equipped kitchen. Only a few hundred meters (yards) is Systrafoss, quite an interesting waterfall (and a small forest). If you are looking for cheaper and less equipped alternative, kemp Kleifar-Mörk can be your best bet.
How to Find Kirkjubæjarklaustur Kirkjubaer II campsite:
You can find the campsite right in the town of Kirkjubæjarklaustur.
GPS coordinates of Kirkjubaer II campsite: 63.792803, -18.049809 Take me there!