One of the best experiences I have had in Iceland was visiting the volcanic islands in the South-West of Iceland. I took a tour to go there, but you can also go by car as well. There is a group of 18 islands, some smaller than others, but breath-taking. One more advantage of visiting them, it is because it is less crowded.
You can get there by car and then you will take the ferry for about 30 minutes. A round-trip with the ferry is around 4000 isk, which is 40$/person. Once you get to the small harbour they have, you will not see so many people as you do in other places of Iceland. The streets are small, very colorful and quiet. There are only few shops and cafeterias where you can also eat, but the variety is not great. I truly recommend having a food back-up.
If you go there with a tour, then a guide will wait for you in the harbour and take you to see the island. You will make few stops and the tour is a full day tour.
You will go to the Volcano Museum, called Eldheimar or the house of fire where you can find out more information about the eruption that took place there in 1973 and affected the population of the island, when almost 5000 people needed to evacuate. Now, you can still see the signs of the eruption, but the live show they have in Eldheimar will take you directly into that landscape.