Christmas mystery: where the wise men came?

We all remember the gospel story of the birth of Jesus Christ.
We know that this happened in the city of Bethlehem, in the cave where they kept cattle.
Also read in the Gospel of the three wise men:

When Jesus was born in Bethlehem of Judea in the days of King Herod, the wise men came to Jerusalem from the east and say where that is born King of the Jews? for we have seen his star in the east and have come to worship him. Upon hearing this, King Herod was troubled, and all Jerusalem with him. And he had gathered all the chief priests and scribes of the people together, he demanded of them where Christ should be born? And they said unto him, In Bethlehem of Judaea: for thus it is written by the prophet: 
And you, Bethlehem, land of Judah, are not least among the rulers of Judah, for out of you will come a ruler who upaset my people Israel. 
Then Herod called the Magi secretly and found out from them what time the star appeared, and he sent them to Bethlehem, and said, Go and search diligently for the child, and when you find it, let me know, so that I may come and worship him. They had heard the king, they departed. And lo, the star, which they saw in the east, went before them, till it came and stood over where the young child was. When they saw the star, they rejoiced with exceeding great joy, and went into the house, they saw the young child with Mary his mother, and they fell down and worshiped him; and opening their treasures, they offered him gifts of gold, frankincense and myrrh. And having been warned in a dream not to return to Herod, they departed into another by their country. Gospel of Matthew, Chapter 2

Based on this text, we can assume that the wise men came to the King who was born in Bethlehem. Traditionally, and depict this event:

We see that those who drew these pictures, no doubt: the wise men came to Bethlehem, and even on the same night when Christ was born. Shows a cave, animals, baby in a manger ... Although it is written that the wise men came to the house.
But read on:

When they were gone, - an angel of the Lord appeared to Joseph in a dream, saying, Arise, and take the young child and his mother, and flee into Egypt, and be thou there until I bring thee word: for Herod will seek the young child to destroy him. He got up, took the child and his mother by night and departed into Egypt: And was there until the death of Herod: that it might be fulfilled which was spoken of the Lord by the prophet, saying, Out of Egypt have I called my son. Then Herod, when he saw that he was mocked of the wise men, was exceeding wroth, and sent and slew all the male children in Bethlehem and in all the coasts thereof, from two years old and under, according to the time which he had ascertained from the wise men.   Gospel of Matthew, Chapter 2
Question: why Herod ordered the destruction of babies in Bethlehem from two years old? The answer here: time which he had ascertained from the wise men.  

Hence, Herod did not know exactly when he was born his rival, the new King of the Jews. He only knew that the birth was going to happen in Bethlehem, and the time when the star appeared in the sky, behind which were the wise men. Therefore, he admitted that the star, the news of the birth of the new King, maybe even two years ago. What did the the wise men two years - it is clear - they were in the way, followed the star from afar, from the East (as the researchers believe - from Persia). But it is clear that the Holy Family might not be as much time in the cave with the animals. Yes, and a child aged two years, does not require a finding in a manger :)
Here we have to remember why and how Mary and Joseph were in Bethlehem? They came from Nazareth in the census because of their race comes out of this town. Of course, after the census and the birth of a child, they had to go back to Nazareth. Not immediately - because according to the law of Moses on the eighth day of a newborn baby boy should be cut off, and after days of purification to come to the temple:

And when eight days were fulfilled to circumcise the child, gave him the name Jesus, named of the angel before he was conceived in the womb. 
And when the days of her purification according to the law of Moses, they brought him to Jerusalem to present him to the Lord 
as prescribed in the law of the Lord, Every male that opens the womb, to the Lord; 
And to offer a sacrifice according to that which is said in the law of the Lord, A pair of turtledoves, or two young pigeons. The Gospel of Luke, chapter 2

After Jerusalem Joseph and Mary was no more need to go back to Bethlehem, so they are back to where they came from:

And when they had performed all things according to the law of the Lord, they returned into Galilee, to their own city Nazareth. The Gospel of Luke, chapter 2

So Herod was wrong in thinking that the new King of the Jews still is still in Bethlehem, but the wise men and more followed the star that led them exactly to the child, that is - in the home of Joseph and Mary in Nazareth!