I like your idea of varying social levels for different parts of the city, but i don't think it need be a vertical structure.

If we keep the buildings on the lake idea, this could be a high class neighborhood, but then so could the towers high above, and perhaps a palace in one of the the deep caverns.

I think we can take this idea one step further. In addition to varying social status in different districts, different regions of the city could have varying tech levels. An example would be a district of the city that has the gates to the planes of fire and water like you suggested using steam power, but the Undead district you proposed would utilize negative energy as the basis of it's tech.

BTW: I love the idea of an Undead district. I'm a big Necromancy fan.