As someone who's experimented and theorized this idea thoroughly, you must understand that Stormwind already has various crime syndicates developed. What I propose you do is simply bring them out and have them represented by the players. It is a common misconception that there is only one gang in Stormwind, just as one may think that there are no gangs in Silvermoon. The truth of the matter is that there are dozens upon dozens, however it is impractical to have them all represented in the world provided to us by Blizzard; that's where we come in.
It's important to leave the largest two groups to NPC's and for Game Masters to have primary control over since these two groups will have the most power in Stormwind:
The Reds
The Defias is so much in numbers and power, it is thoroughly represented by Blizzard and serves as a general represenative and example for crime in Stormwind City. It's boundries go beyond that of simply Stormwind and have created an intricate circle of various crimes. The Defias are generally despised by smaller chain gangs, but they're respected among the community of criminals.
The Grays
The Grays are the nicknames given to the Guards, but it generally refers to the government in itself. The Grays are extremely powerful in their organization, training and in their position of legal power. This force is quelled by the need to uphold the law and restricts them to retaining rather than killing on sight.
Another group may arguably be the Syndicate, but realistically their presence in Stormwind is nominal in comparison to the other two. It is also important to note that direct war with either of these two groups is suicidal, and is best that they are treated indirectly in almost all cases.
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There are, unfortunately, a lot of people here who don't know what they're talking about and are giving very impractical and (reasonably) unintelligible advice, or atleast from the level that I am used to.
If you want my "professional" opinion, which I merit with experience in this realm of RolePlay, I believe that giving a whole district to a single guild is too much; fractionalize districts and have guilds control it as "turf". If the turf runs across whole districts, there are several problems with that; lack of representation by the Guards and Defias (AKA, controlling the whole Old Town district by one gang would mean that the military fort there is on that gangs turf) and also it would delay conflict and minimize friction (things get hotter when you're compressed in a tighter space). Let guilds gain power by the willingness of the players rather than having to use NPC's and be open to character death, torture, and so on. Make sure guilds are
SMALL and LOCAL, because if they're big, then they're infringing lore by implying major signifigance. If it challenges half of the power of the Defias, it needs to be nerfed.
Your best bet, and most successful bet will be in Old Town, where crime is already rampant; the Mages district is complicated because of the large population of intelligent magic-wielders and scholars who either don't have the time for crime (via studying) or are busy commiting high crimes beyond the normal spectrum of a non-magic wielder. Warlocks are notorious in the region for having connections to criminal operations, however they are met with distrust, probably because most dolts who are silly enough to trust a Warlock become an experiment, or are fed to some nasty experiment, or worse love (light term) in a masochistic form, which is often imposed upon without consent. The Dwarven District is more than likely one of the first places thought to be a crime hotspot, but in reality, when examining Dwarven culture and how they deal with their criminals (severely), it is unlikely that it is spewing gangs; at the most, I believe there would be gangs occupying the southern portion of the Dwarven District, as to represent its origins from Old Town. The Trade District is enforced very tightly; gang presence there is not likely at all, unless they take presence as a company. The thing about the Trade District is that it's where all the money is; if it is economically unstable due to crime, then Stormwind will falter. The presence of the guard is magnified by the two high ranking guards who sit in the center of it, and generally represents that the only real crime in the area that happens is in the alley ways or in private residences and warehouses, which don't make good for gang locations since they can be checked (and will be) as a counterstrike against smuggling. The Harbour is contested territory (as is Old Town) between the Grays and various criminal organizations, but is segregated from the rest of the city in a way and is better seen as an auxillary location until we have a sufficient presence of gangs. The Park is a questionable entity; I would assume most gangs would avoid it, knowing that if they interfere with the political relationship between the Elves and Humans, the Grays will be very protective. Ventures probably come with mixed results, but more than probably are less profitable; Night Elves, contrary to popular belief, are not very fond of capitalism nor the crime in general.
If you're considering being serious about crime in Stormwind, it's a subject I've touched. Terms such as the "Stromgarde Smile"
or the "Booty Bay Bowtie"
can be used to ensure realism is cupped in place, and to add more colour to the environment. Different gangs that centralize on a specific crime; pimping, slaving, smuggling, murdering, stealing, information, bruising, torturing, bribing-- Although, it's important to keep in mind that the gang should be well rounded in some sense of the form.
Regardless to whether you read, or use what I've provided, know that it's been tested, proved and is, from what I know, the most mature and realistic method.
In any case, I'll (re)make Tenissa (infamous criminal mind/flamboyant pimp) to be the general IC guru for your characters to ask advice and so on. His vast connections, which gangs can take advantage of, will extend the ability to assassinate, buy drugs in bulk, etc. Just make sure I know he's wanted. If anyone else wants to take a similar role, you can contact me by PM and discuss creating a guild for this as a sort of glue for the rest; the "elites" of special skill criminals who don't need to seriously associate themselves with a single gang, but band together to maximize connections and keep the gears running. It's a much lower priority relative to the gang guilds, but it requires larger amounts of experience and intuitiveness.
EDIT: Re-read, I forgot to mention the harbour, park and Warlocks.