Grenen is the actual northernmost point of Denmark — a long curving sandbar where the Skagerrak and the Kattegat collide in waves that visibly clash with each other. Getting there requires a 20-minute walk (or a ride on the Sandormen tractor-bus) across open beach from the car park, then a scramble along the narrowing spit.
The spot itself is low and exposed, with nothing between you and the North Sea. The two seas really do look different — different colours on a good day, different textures, different directions of swell. On the way back, the views south along Skagen's west beach are excellent: long, pale, and very empty.