Stokknes is a promontory a couple of miles north of Höfn below the Vestrahorn mountain. To get to Stokksnes (coming from Höfn) you need to take a right before the tunnel on road #1 going north. There is a gravel road that leads to a small cafe called the Viking Cafe. The land is privately owned therefore is is necessary to pay a fee of 800ISK per person to be able to go to the black dunes and the beach of Stokksnes.
There is no way around the fee as the beach is secured with a gate and several barriers. The gate will open if you scan your ticket! We had to buy a ticket twice cause the first day we went there the storm was so bad at the beach that we could not leave the car. It was really creepy weather and soon after we left it started snowing really bad.
After the snow storm the night before we deciced to try our luck again and it worked. It was sunny and a lot less windy. We were able to take lovely pictures and spend almost 2 hours at the beach and in the dunes.