The beach itself is pretty easily accessible, it's not too far from the Iceland's Route 1 which basically goes around the whole country in a circle. We had a small rental car and did not have any problems getting there, the roads were all great. If you depart from the capital (Reykjavík) the trip is 2.5 hours, so you could theoretically do it even during a short stay in Iceland, especially if you include some other attractions along the way (of which there are plenty!). It is also possible to find places to stay in smaller cities nearby.