It's difficult to interpret what you're getting at when you say "explorers of the ancient world". Alexandria was the main cultural hub of the eastern Mediterranean in Greek antiquity, so it would be extremely unsurprising to find almost anyone in that part of the world visiting the city. It's a bit like asking if any 20th century explorers might have visited New York.

As to the library, here's the usual caution: Alexandria was just one research centre among many in the Greek world. It was the largest library, at least prior to 48/47 BCE, but certainly far from unique. There were plenty of other places to do research. For a parallel think of it as, say, the British Library, in a world where you've also got libraries at Oxford, Cambridge, Dublin, Manchester, etc. to play in; or the Library of Congress, in a world that also contains the libraries of Princeton, Chicago, Harvard, UCLA, etc.

Timeline:

• 331/0 BCE: founding of Alexandria

• 307: Demetrios of Phaleron leaves Athens; subsequently he settles in Alexandria, and is appointed by Ptolemy I Soter to be the first director of the Mouseion (the cultural/research centre that accommodated at least part of the libraries). The collections are divided into a royal archive and a public library. We also hear that the collections were divided between one archive in the Brouchion, and another "daughter" library at the temple of Serapis. It therefore seems that the latter was the public collection; the practice of using a temple to house texts had precedents going back at least a thousand years. Some scholars believe that the Serapeion was only an overflow annex, but one key (and nearly contemporary) source reports that there were separate royal and public archives from Demetrios' time onwards.

• A very doubtful source (the "letter of Aristeas") reports a story of one occasion when Demetrios informed Ptolemy that the library supposedly contained over 200,000 books, and that he hoped to make this number up to 500,000. The letter is largely a fraud, however, and dates to the 100s.

• 1st half of 3rd century: Kallimachos of Cyrene compiles his Pinakes, an account of the library's collection. The text is lost, but one witness reports that according to Kallimachos, the public archive contained 42,800 books, while the royal one contained 400,000 miscellanies and 90,000 single-text books.

• 200s: Demetrios is succeeded by several people as director of the Mouseion: Apollonios of Rhodes (student of Kallimachos), Eratosthenes of Cyrene, Aristophanes of Byzantium.

• 145: spat when Ptolemy VIII temporarily expels foreign scholars from Alexandria.

• 1st century BCE: heyday of Alexandria as research capital of the Mediterranean

• 48/7: Julius Caesar attacks Alexandria and a large part of the libraries -- presumably the royal archive, since there is a much later description of the Serapeion library -- gets burned in the kerfuffle.

• Sometime between 41 and 31 BCE: Mark Antony supposedly makes a gift of 200,000 volumes from the library of Pergamon to Cleopatra. (Plutarch is our source for this, so take it with a pinch of salt.)

After this there's a big gap in the chronology, presumably as a result of the Roman conquest. There were still thinkers and teachers going there and living there, so it still possessed some prestige as a research centre, but the stories about famous scholars dissipate.

• (272 CE: civil strife in Alexandria during Aurelian's invasion)

• (295: Diocletian visits Alexandria)

• 315: visit by Aphthonios, who provides the best surviving description of the Serapeion and the library.

• 391/2: fire; Theophilos storms the Serapeion. Some people doubt that the library was still housed there at this point, since it's not mentioned.

• (415: lynching of Hypatia; it's very doubtful whether any significant library still existed at this point)

• (600s: legend has it that 'Amr ibn al-'As burned what remained of the library at this point; but this is moral fable, not history)

We don't have any sustained accounts of the library, so most of these points are derived from isolated references in other works. As a result most of them are debateable. But do please bear in mind the caution in my second paragraph: there were loads of libraries in antiquity.