"We hurry out to the new airport."
Translation:Kisietünk az új repülőtérre.
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.