In Iceland you have a very generous varity of camping sites (see https://tjalda.is/en/). Almost all villages around the country offer a camping site with amenities like showers and toilets. Also in the highlands there are camping sites. Please note that some camping sites are not open during the winter season.
There is no need to book in advance at camping sites.
The cost varies as well as the facilities but is usually around EUR 10 per night per personBack