The real world city of
Budapest gives another way to do a city in a dungeon. Much of Budapest used the natural cave system for basements. Later they connected many of the basements to each other. There were times in the past when the weather was foul or topside was dangerous when people could travel across the old city of Buda (pest was the German town on the other side of the river) through the caves under the streets.
In a dungeon fantasy world the levels just below the city would be a border area before you got to the real dungeon/wilderness below. Respectable houses of top, seedy taverns and questionable establishments beneath these, and the dungeons below these.