Put your thinking cap on now. Imagine that the Gulf Of Mexico was blockaded from the world's oceans at the height of the Ice Age. The world's oceans would stabilize (water depth) at 300-500ft below present levels while the Gulf Of Mexico (now blockaded) would continue to dry out and then finally stablize at a level much below the worlds oceans during the Ice Age.
This 'underwater' city was built on dry land on the shore of the dessicated Gulf Of Mexico thousands of years ago. Once the ice from the Ice Age began to melt and the water levels of the worlds oceans began to rise, the rising water reached a level that would breech the blocade to the Gulf Of Mexico and cause a catastrophic flood (like the Black Sea) and anything on the shoreline would now be hundreds of feet underwater. I came up with this idea after reading about the Black Sea flood and realizing that a half mile is a long way for something to 'sink.'
There are probably ancient 'underwater' cities all over the globe.
It would help to know the precise coordinates of the "sunken city", but the popular accounts that I've seen don't provide that information.