"THROUGH RELIABLE SOURCES SHAYKH AL-TUSI HAD NARRATED A TRADITION FROM IMAM ZAYN-AL-ABIDIN THAT THE PLACE DESCRIBED AS A "FAR-OFF" PLACE BY ALLAH WHERE MARYAM HAD MOVED FOR DELIVERING ISA (A.S.) IS KARBALA. Maryam had covered a long distance from Damascus to Karbala in a split second; ISA (A.S.) WAS BORN AT A POINT NEAR THE GRAVE OF IMAM AL-HUSAYN and she returned to Damascus that same night."
"In al-Qutb al-Rawandi narrated from Yahya bin Abdullah that, "I was with imam Jafar Sadiq (pbuh) in Heerah. One day we went riding and reached a village in the VICINITY OF NASIRAH AND CAME NEAR THE EUPHRATES." IMAM said, "HERE IT IS, HERE IT IS," and then dismounted, prayed two Rak'ahs of prayers and asked me, "DO YOU KNOW WHERE ISA WAS BORN?" I said, "No." He said, "IT IS HERE, WHERE I AM NOW SITTING." Then he said, "Where was the palm tree which was shaken by Maryam for its fruits?".....
And mention, [O Muhammad], in the Book [the story of] Mary, when she withdrew from her family TO A PLACE TOWARD THE EAST. (Surah Maryam 19:16)
The place where He (Isa pbuh) was born (as mentioned in the Quran) was in the East. As we can see from the hadeeths of Ahlulbayt(pbut) the meaning of East in Surah Maryam is present-day of Iraq.