Random time...Yes I think so.

Father Clifford in his sermon about Saint Monica says that Great Lanta is 'on the shores of the ocean.' I've always thought that maybe it was Atlanta he was talking about and something weird happened because of the great war. I put that on the Wiki though and someone edited saying it was probably Atlantic City. There's also the possibility that Father Clifford is just an idiot, mistaken about geography just like Abraham Washington is about history.

Which one do you think it is?

I imagine it's Atlantic City, it just seems to fit better and it is closer to DC than Atlanta is.

I dont see why it would have to be near DC It is possible that it was a city built after the war

Lantana, Florida

Maybe, before the war, Atlanta was moved to the Georgia coast, to open up a sea port or harbour.
It could be similar to the Futurama episode where Atlanta was moved to the Atlantic Ocean.

Yes but news doesn't travel great distances well or quickly any more so someone in DC is more likely to have heard of a settlement in Atlantic City than Atlanta. Most of the large settlements we hear about in FO3 are in the north east: Pittsburgh, Toronto, and Boston. So Atlantic City is in the same general region we're hearing about.

This doesn't mean that it's unreasonable that someone in DC would have heard about a settlement in Atlanta but since Atlantic City is closer and since it's actually on the water it seems more likely.

Ah yes I forgot that there would be difficulty for news to travel in a post-apocolyptic wasteland. I am unfamiliar with American geography Im afraid