Did the star lead the Magi to King Herod in Jerusalem?

Well, not exactly. Matthew 2:

1 After Jesus was born in Bethlehem in Judea, during the time of King Herod, Magi a from the east came to Jerusalem 2 and asked, “Where is the one who has been born king of the Jews? We saw his star when it rose and have come to worship him.”

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They saw the unusual star. They knew that the star signified a new king being born of the Jews. Naturally, they headed for Jerusalem, the capital of the Jews, to look for him. The star's position at this point did not specifically indicate the city of Jerusalem; rather, the star showed them the general direction.

They asked King Herod, but he didn't know. Herod asked the chief priests. They told him Bethlehem.

8 And he sent them to Bethlehem, saying, “Go and search diligently for the child, and when you have found him, bring me word, that I too may come and worship him.” 9After listening to the king, they went on their way. And behold, the star that they had seen when it rose went before them until it came to rest over the place where the child was.

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The star confirmed the destination was Bethlehem. Now, the star position precisely led them to the place where baby Jesus was. They didn't need to ask the locals.