Thanks to Wikipedia I can relate the basic story,
"For it is related in our records how once upon a time your State stayed the course of a mighty host, which, starting from a distant point in the Atlantic ocean, was insolently advancing to attack the whole of Europe, and Asia to boot. For the ocean there was at that time navigable; for in front of the mouth which you Greeks call, as you say, 'the pillars of Heracles,' there lay an island which was larger than Libya and Asia together; and it was possible for the travelers of that time to cross from it to the other islands, and from the islands to the whole of the continent over against them which encompasses that veritable ocean. For all that we have here, lying within the mouth of which we speak, is evidently a haven having a narrow entrance; but that yonder is a real ocean, and the land surrounding it may most rightly be called, in the fullest and truest sense, a continent. Now in this island of Atlantis there existed a confederation of kings, of great and marvelous power, which held sway over all the island, and over many other islands also and parts of the continent.
But at a later time there occurred portentous earthquakes and floods, and one grievous day and night befell them, when the whole body of your warriors was swallowed up by the earth, and the island of Atlantis in like manner was swallowed up by the sea and vanished; wherefore also the ocean at that spot has now become impassable and unsearchable, being blocked up by the shoal mud which the island created as it settled down.
Perhaps the stupidest Atlantis search I ever heard about was on a TV show where some guy reasoned that there was no large land mass beyond the Pillars of Heracles (Hercules in Latin) then Atlantis had to be in South America. He found a Toltec or Mayan ruin and then using the kind of convoluted logic that these kind of obsessed people have, he calculated that a cubit was a different length at that latitude, I think shorter, so when using that measure the dimensions came out as written in the legend.
Did the Atlanteans know that the earth is round? They were supposed to be advanced, but would they have known that they were supposed to change the length of their measuring sticks when they founded the city? “Hey, bubbastotle. You need to cut your cubit stick shorter.”
“What are you talking about?”
“BillyBobatsophanes says that at this latitude cubits are shorter.”
“Just cut off 10 decicubes.”
“But this cubit stick has been passed down in my family for generations”
"Well now you can pass down a shorter cubit stick.”
The guy only paid attention to the parts of the story that suited him. He didn’t notice, “an island comprising mostly mountains in the northern portions and along the shore, and encompassing a great plain of an oblong shape in the south ‘extending in one direction three thousand stadia [about 555 km; 345 mi], but across the center inland it was two thousand stadia [about 370 km; 230 mi].’ Fifty stadia [9 km; 6 mi] from the coast was a mountain that was low on all sides...broke it off all round about... the central island itself was five stades in diameter [about 0.92 km; 0.57 mi].”
I don’t know what stadia are, but I’m sure that that description is of a land mass much shorter smaller than South America And could a city on the other side of the Atlantic attack the European mainland and threaten Athens? There were no ships at that time capable of making a transatlantic voyage. How do I know? Archeologists have found ships from that era. Many of which are shipwrecked in the middle of the Mediterranean. People had a hard enough time sailing around in the Mediterranean sea, much less the Atlantic. Odysseus spent ten years wondering around a small area, and the Argonauts that it was a big deal going to the Black Sea. Nor do they find any evidence of Ocean going craft in South America.
Then what about "wherefore also the ocean at that spot has now become impassable and unsearchable, being blocked up by the shoal mud which the island created as it settled down." One key part of the Atlantean story is that the continent sank. This guy found a ruin on dry land.