People paint it as Greek because it's a Greek myth, even though it is explicitly supposed to be a foreign culture that predates it by several thousand years (despite also being at war with Athens at some point).
would probably be a more suitable aesthetic inspiration if one wanted to copy something, as the original allegory Plato was going for was in reference to the Minoan eruption, which was a more recent case of an island being devastated by natural disaster.
Of course, the difference being that Atlantis is supposed to be an island the size of Texas in the middle of the Atlantic, so if anything it should be vastly different. In terms of seafaring trade-routes, it might make sense to draw upon Phoenician architecture or even some stuff from further north in Europe, but of course the alleged timescale doesn't quite line up with that if Atlantis was supposed to be thriving at 9000+ BC, during which time everyone else is stone age so there's no good neighbors for them to share designs with.
One easy answer there is to pick a nearby ancient civilization and have them be descendants of Atlantis, and therefore say that their architectural style is inherited from them, but really the timescale we're talking about is massive.
In terms of actual physical description, the most you get is of the main city, which had ringed walls of brass, tin, and orichalcum (which according to the myth is basically brass but more red), so you could expand upon that to have a lot of metalwork involved in their architecture, but that just gives you material rather than actual design.