When I was brought up, I was told to face East when starting some new task or while doing prayers or chanting mantras. My guess is that it might have come out of ancient sun(Surya) worship as sun rises in the east. Is there any real significance for considering the Eastern direction to be auspicious?
It is because gods are believed to be present in the east direction of earth:
देवमनुष्या दिशो व्यभजन्त प्राचीं देवा दक्षिणा पितरः प्रतीचीं मनुष्या उदीचीं रुद्रा [Tait. Samh. - 6.1.1]
Gods and men divided the directions. Gods took the east, pitaras (manes) took the south, men took the west and rudras took the north.
So while worshiping or praying to the gods, a person generally has to face to the east direction.