This is Columbia, the city featured in the video game Bioshock: Infinite. It stands out in that this city floats in Earth's atmosphere. How? Some sci-fi handwavium called "the Lutece Particle". This sounded like the sort of thing we'd associate the future with, except that in the game, Columbia was afloat in 1893. Considering the limited technology, knowledge and resource access of the time, this is completely unlikely, and the Lutece handwavium I can dismiss as "anachronistic cheating".
Before I ask as to how to create such an atmospheric city realistically, my first question is this--what point of departure must happen to make floating cities like Columbia a reality? Could be any time period, not just 19th century like in Columbia.