a relaxing holiday = ein erholsamer Urlaub
gehen auf einen Urlaub is the translation in German. It is translated from English to German. German is mostly spoken in the European countries.
Fun vacation in German is (lusticas ferien)
Ferien
The one who leaves, as the one who stays not necessarily knows you are going somewhere.
sto andando in vacanza
Me voy de vacaciones.
Ich gehe
Sweden
I am going dancing = ich gehe Tanzen
If you are going to the beach you might say "beach hoilday", but if you are going somewhere else you could just say you are going on "hoilday" or vacation.
afthaltr dad goot
Wohin gehen wir?
I am going to the Fatherland = Ich gehe zum Vaterland.