Here's a short list of factions within Denethix. I'll be using these to "wing it" with city encounters.
City Council - this is the Vizier's faction. The council has 40 members, and the Vizier controls them through the use of committee chairmanships, which he appoints. These committee chairs provide significant additional income, as well as ample opportunities for bribes. The chairmen are thus bought-and-paid-for by the Vizier, and they in turn bully the lesser councilmen by refusing to pass whatever legislation interests them unless they "play ball."
Wizard's Guard - the Captain of the Guard's faction. The Vizier and the Captain are both politically competitive, and in cahoots, as neither wants to risk anybody ever finding out about the wizard's true condition.
Tax Collectors - this arm of the bureaucracy collects tariffs and taxes. Wherever there's money, there's corruption - these fellows are rotten through-and-through. A healthy portion of collected taxes goes straight into their pockets, and an even larger sum is paid to the councilmen and the wizard's guard. Whatever remains is spent on the city budget. The actual processes are opaque, and the collectors are not popular in the city. Somebody has to gets their hands dirty, though. The collectors are chafing at the amount of money the council and guard are extorting from them, and would love to find a way to get them to back off.
Abolitionists - a little freedom breeds the desire for more. The Abolitionists are an underground movement in Denethix, and desire the freedom of all slaves in the city, and the overthrow of the wizard. They are in constant conflict with the council and the guard, whom they consider corrupt. They are not pacifists, and showdowns between them and the guard often turn bloody.
Church of Starry Wisdom - they want what the Crawling Chaos wants, which is to open men's minds to the true nature of the outer spheres. This is not compatible with a functioning city government, or sanity in general.
Bankers - Kingdoms far from the Land of the Thousand Towers rise and fall on the Bankers' whims. The Wizards themselves have no interest in commerce or filthy lucre, and the Bankers have little interest in super-science, so there has been no reason for banking to take hold in this wizard-blighted land. Denethix has the first bank to be established in a Wizard's City-State, and the city is deeply in debt to them. They will ruthlessly manipulate factions within the city to ensure that payments do not fall behind.
I'll have to come up with a few more exotic factions, but it's getting late. I'll create a few more this weekend.