On the western side of Reynisfjall, the high ridge above Vík, Rte 215 leads 5km down to the black-sand beach Reynisfjara. It's backed by an incredible stack of basalt columns that look like a magical church organ, and there are outstanding views west to Dyrhólaey. Surrounding cliffs are pocked with caves formed from twisted basalt, and puffins belly-flop into the crashing sea during summer. Immediately offshore are the towering Reynisdrangur sea stacks. At all times watch for rogue waves: people are regularly swept away.
You may recognise the scene from Bon Iver's 2011 music video Holocene, practically an ode to Iceland. The beach can get busy in high season, so try to come early in the day or late in the evening.