|Friends don't let friends use detailed city maps. I kid...sort of.|
The short answer is: I run them exactly like any other adventure.
In other words, I come up with a brief scenario that presents a problem that the characters can fix, write up the NPCs they're likely to interact with, the most likely ways they'll be drawn into peril, find some appropriate monster stats, and make myself a flowchart of the way things might shake out (but also leaving room to be surprised by player choices I can't account for). I don't really have a set of procedures for this (when I think of fun game stuff, procedures are not what come to mind), just enough notes to get going and to flesh out what the twists and turns that the game takes.
If the adventure is set in a city or other urban environment, it doesn't really change the basic way I go about things. Here's why: my favorite fantasy novels have always been the ones that didn't come with a map.
It's rare that I look at the lay of the land in a map and find inspiration; that goes double for city maps, which just tend to be named streets and the relative position of buildings. My copy of Perdido Street Station has a map of New Crobuzon in it. Why? The map is at best tertiary to the way the city is unveiled in the text. I don't get the feel of a city from a map; I get the feel of a city from the way it is described, the people who inhabit it, and the ways in which activity and personality intersect. It follows that the way I want to present a fictional city in play would be through description, action, and reaction--not the map.
(As an aside, I find this true of the way I actually experience urban spaces. I can't really learn about a city by reading about it, I have to walk the streets and take in the neighborhoods, residents, and unique features personally. Maps are helpful for navigation, but nothing beats being there.)
This is why I find most "city supplements" for games to be generally unhelpful for me. They tend to present information on the city block-by-block, street-by-street, keyed to a map. Worst case scenario: there will be facts and figures for things like yearly wheat consumption and excise taxation charts. I'd rather present the city through its atmosphere in play: what is happening there, who calls it home, what are the anxieties and hopes that burn eternal, etc.
I might use smaller maps of specific locations within a city because sometimes the position of things matters. But it rarely matters at the medium-and-larger scale in my games. This is also why I don't really do dungeoncrawls or hexcrawls.
For city adventures, I'm not even bothering to make a map of the city. There are practical considerations there, of course, but also that's not how I want players to discover it. I want navigating a fantasy city to be more imaginal than tactical.
Also, I'm fairly lazy and can't be bothered to make a map that big.
As an example of what I'm on about, read K. J. Bishop's The Etched City, which has one of the most evocative fantasy cities as its main setting. Note that there is no map of Ashamoil. Do you feel the absence of a map while you read?
Of course, this is just what works best for me. You might be an entirely different nexus of needs and desires. I'm not the boss of you.