There are two campsites in Kirkjubæjarklaustur, and this one is located right by the Stjórnarfoss waterfall. Don’t expect much luxury here; there’s just a shelter with sinks and two toilets (which have power outlets). On the other hand, it’s one of the cheapest campsites in Iceland. In the town, you’ll find a supermarket where you can stock up on food supplies. If this campsite doesn’t meet your needs, there is another, much better-equipped campsite, Kirkjubaer II, nearby in the village.
You can find the campsite along road no. 203.