I can't think of anything that quite fits. "Kos deg" is probably be what I would say in a similar situation, but the actual meaning of that is closer to "enjoy yourself" than "have fun".
"Ha det gøy" fits the meaning better, but doesn't feel as natural to me. I think I've heard it, but I can't remember saying it. I think I would have to tack something on to the end to be comfortable with it..."Ha det gøy i morgen!" or "Ha det gøy i Bergen" sounds OK.
Tusen takk for det NNYC!Since there is no specific way of saying this in Norwegian, one has several options: ha det gøy/kult/fint/kjekt and many more