We’ll be staying in Viborg for two nights and want to spend one full day driving around North Jutland. Are there any must-see places or routes to take?
Northern dune beaches between Blokhus and Hirtshals are worth seeing, esp. Rubjerg Knude Fyr (a lighthouse) which sometimes partly disappear in dunes. Partly the beaches are open to drive on along the coast, e. g. Saltum Strand.
Grenen close to Skagen is the "melting point" between North and Baltic Sea.
Skagen's Museum is worth a visit.
If you are interested in history a visit to Sea War Museum Jutland is an option as well as visiting the museum frigate Jylland in Ebeltoft from a different time.
Some more tips you will find in this article.
And don't forget to find a reasonable good fish restaurant for lunch (fiskefillet) and to eat a Danish softice cream (my favorite brand is Polar Is).
What are you interested in and what are you looking for?
Interested in natural scenery, a WW2 bunker, small towns and a seafood lunch or dinner.
Rests of WW2 bunkers you will find a lot along the North Sea coast line, e. g. Vigsø Battery or bunker radio station Lyngby and batteries north of Lyngby.
Maybe you consider visiting Bunker Museum in Hanstholm?