Right nearby Dyrhólaey you'll find this beautiful view. I don't know why these aren't better known the masses since the views from here are amazing in every direction, and it's different everytime you visit. Only a short drive from Reynisfjara Beach (better known as Black Sand Beach), which is one of the views.
Coming from the ring road, just follow the sign "⌘ Dyrhólaey", after a few minutes the road might just be covered with water as it's on almost the same level of the road! It's almost always safe to just drive through it, even if you don't have a 4WD. Just follow the road all the way up until you reach the parking lot. There's a few paths going down, but you can't really get lost there. Just enjoy all the different views!