Jerusalem being the capital of a province of his empire, that he passed by at least twice going to and returning from Egypt, it seems most unlikely that Alexander didn't visit Jerusalem. He apparently went out of his way to visit the Siwa Oasis (where his god-hood was confirmed) after founding Alexandria.
Chapter Eight of Volume XI of Josephus describes the entry of Alexander into Jerusalem in somewhat fantastic terms, but there doesn't seem an obvious reason why this would be manufactured.
.... And when the Book of Daniel was showed him [Alexander] wherein Daniel declared that one of the Greeks should destroy the empire of the Persians, he supposed that himself was the person intended. And as he was then glad, he dismissed the multitude for the present; but the next day he called them to him, and bid them ask what favors they pleased of him; whereupon the high priest desired that they might enjoy the laws of their forefathers, and might pay no tribute on the seventh year. He granted all they desired. ....
Felix Goldberg below raises good points about the veracity of Josephus' story above.
- Compared to visiting the Siwa Oasis - 10-14 days travel due south into the Libyan desert, don't get lost in that featureless waste or you die - a quick jaunt from Gaza to Jerusalem is nothing.
- Alexander was vain - he seems to go anywhere, and do anything, to have his divine destiny to overthrow the Persians reaffirmed. As evidence, note point (1) above.
Certainly the story by Josephus is fanciful, and undoubtedly exaggerated in its details; but I still see no reason to doubt it's core, given Alexander's demonstrated vanity for this sort of attention. Just a whisper in his ear that the Jews had a holy book in a great temple foretelling a Greek defeating the Persians, and I think he would have postponed even a battle to visit in person.