An excerpt from an Arutz Sheva touristy sort of thing on the tomb of Shimon (and related activities):

The Talmud relates the famous story of the meeting between Alexander the Great, the world-conquering Macedonian Emperor, and Shimon HaTzaddik. At the behest of Jew-haters, Alexander marched on Jerusalem, with intent to destroy it. Shimon the High Priest donned the White Priestly Garments that he wore on Yom Kippur when he would enter the Holy of Holies, and went out to meet Alexander. To the surprise of his entourage, when the Emperor saw Shimon HaTzaddik, he dismounted and prostrated himself before Shimon. Alexander's generals asked him why he was bowing to this Jew, to which he replied that every night before a battle, he would see in a dream the figure of that Jewish High Priest, who would advise him on tactics to use the following day - a service that never failed him.

Shimon HaTzaddik took Alexander the Great on a tour of the Temple. Alexander was very impressed and requested that a marble image of himself be placed in the Temple courtyard. Shimon explained that it was forbidden for the Jews to have images, and certainly not in the Temple, but he suggested an alternative way giving homage to the Emperor: that all male babies born that year would receive the name "Alexander." The Emperor accepted, and that is how "Alexander" became a Jewish name.