The volcano is situated approximately 30 km from the country's capital city, Reykjavík.
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With a little preparation you can visit the volcano yourself. Drive to the trail head and follow the easily marked hiking trail to the volcano viewing site. You are always responsible for your own safety when you hike unaccompanied in Iceland.
When we went over the summer when the volcano was still active we did a self tour, i.e., we followed the very obvious path to the lava field. I would not recommend paying anyone to take you to see the lava field.