Accommodations in the coming summer and autumn are filling up in many areas in Iceland. The most popular tourist areas like the south coast from Vík to Egilsstaðir in the east hardly have any places left with private bathrooms.
Do not despair! Iceland is more than the south! The west as beautiful as it is has usually very few tourists. The reason is not that it is not as beautiful it is because it just isn't adverized as much. It is one of the least touched sights in the country.
The north has also a lot of accommodations and few of the most famous places in Iceland. Akureyri, often called the capital of the north has many good accommodations and offers great opportunities to visit these sights in day tours from there.