"We hurry out to the new airport."
Translation:Kisietünk az új repülőtérre.
the same exact sentence (but from Hungarian to English) was using repülötérhoz. Now hoz is rejected. Can someone explain why, please
Repülőtérhez. There is nothing actually wrong with saying "repülőtérhez", but be aware that it does NOT mean what "to the airport" usually means, that is, actually being at the airport as a passenger, etc. "A repülőtérhez" means that you would be close to, but not at, the airport.
The verbal prefixes are sometimes split from the root verb. It depends on what you want to say.
There is only one sentence at the top of this page, and it uses 'kisietünk'. What is the sentence that you mention that uses 'sietünk ki'? Please tell us, so we can answer your question.
Compare this with the students who were supposedly coming out to the airport even though we had no idea where they were coming from and thus el, oda, at or ki would have worked. Here we are told. It's out and therefore no guessing required.