I would recommend not staying at the official campsite at the Skaftafell Visitors Centre. The site has increadibly poor drainage and when it rains, which it does a lot in Iceland, it tends to get very waterlogged. There is another campsite a little further east along the main road which is on a slight slope meaning it doesn't suffer from this problem. This campsite also has a swimming pool and hot-tubs, which are great after a day in the mountains.