Explore the island driving the circle road. If your car rental allows use some F-roads for detours to visit Landmannalaugar.
The road takes you to different waterfalls like Godafoss, Detifoss and Skógafoss. Other sights like Dyrhólaey cliffs, Jökulsárlón glacier lagoon and Myvatn is very accessible.
Tour the Snæfellsnes peninsula driving up to the Snæfellsjökull Glacier, a visit to the small town of Arnarstapi and Mount Kirkjufell.