Seems like there is several questions that will effect a lot of the answers you can give as to how an underground city and/or region would be laid out on a map.

How far underground and how self sufficient?: Is the settlement either easily reached by straight large paths or only a small ways underground so that most of the resources such as food and air within easy reach, or are these subterranean cities deep underground with no, limited, or time and resource intensive access to the surface? There is of course a wide spectrum between those. The later seems to require more modifications to the real world than the former which is easily accomplished. A map of someplace built underground to take advantage of valuable but fairly easily reached resources or built into a hill for protection seems like it would look little different from the map THW posted or like an ancient mine complex. More vertical but otherwise with few features different than any city map.

How human like are the inhabitants and how earth like is the world?: Are we talking fantasy dwarves, scifi aliens, or something between the two? A fantasy race or scifi race that doesn't look almost completely human but was actually adapted to living underground (probably look a bit like everything that takes up this life style moles, mole cricket, fairy armadillo, etc.) then they won't be in fear of needing heat except for the use of it in the civilized pursuits of material science and getting the most nutrition out of food (or if they were from deeper still and found the colder temperatures further from the truly deep underground a bit chilly). Presumably they wouldn't need it for light either as few of the worlds subterranean inhabitants are big on it. More human like races will need far more of the things we do: heat, light, better ventilation. All this of course can be changed on less earth like world with different resources available be it from ecosystem, geology, or magic (hopefully the kind that creates as many problems as it solves because simple hand waving is boring). How common giant caves or tunnels leading between subterranean areas are will effect transportation and expansion a lot also. If these changes are included they will give you a very different layout depending on how abundant these resources are and how they fall in the world.

What material sciences are available?: Most fantasy races seem to spring into the world with fully developed material sciences that allow them to live where they do, and why not if the gods made them for it? Less divine races will need to develop their technology in a more reasonable way with the available resources underground if that's where they started or by taking above ground inventions and re-purposing them for their new life style. If you want dwarves that can breath using only ancient technology, the water wheel and the windmill are both ancient enough to reasonably appear in at fantastic setting, though it would be novel to use the sails of the windmill to push rather than catch the wind. Other worlds and other resources would spawn entirely different sets of answers as to how to accomplish the same thing.

Ok my head is filling with an obsessive desire to to fill in increasingly smaller details so I had better stop for now.