Take one of the many (and often cheap) flights departing from Copenhagen to Aalbort and rent a car in Aalborg Airport.
Car rental in Aalborg Airport: http://www.aal.dk/Forside/Billeje/
Find a route description on www.krak.dk
Traveling tip: Take the road which the locals use to avoid the holiday traffic. Take the motor way towards Hirtshals in stead of towards Frederikshavn. In the large roundabout close to Hirtshals turn right and follow the signs towards Skagen.
From Copenhagen/Odense/Århus: Take an Intercity-train towards Frederikshavn and change to lokalbane towards Skagen. www.dsb.dk
Hotel Plesner lies about 100 m from Skagen Station.
From Göteborg: Take the ferry from Göteborg to Frederikshavn and drive via Ålbæk to Skagen. http://www.stenaline.dk/faerge/ruter-og-destinationer/frederikshavn-goeteborg/
From Oslo: Take the ferry from Oslo to Frederikshavn and drive via Ålbæk to Skagen.
From Kristianssand: Take the ferry to Hirtshals and drive to Skagen. http://www.colorline.dk/fartplan_og_ruter/hirtshals-kristiansand
Skagen Taxa: Phone +45 9843 3434
Frederikshavn Taxa: Phone +45 9842 1311
Vendsyssel Taxa: Phone +45 9656 5656