"Does this share taxi go to the post office?"
Translation:Ця маршрутка їде на пошту?
I would say it sounds even more correct. на пошту is used more commonly in the context of a person heading to a destination where they are going to do something, like "I'm going to the post office" - "Я іду на пошту" (to send a letter), but "Я іду до пошти" (to meet with someone at the entrance, for example, where the post office serves only as a landmark). Here, до пошти will be preferable.