politics breeds violence. they no doubt play their game via proxies, both known and unknown. perhaps a doppleganger 'family' enters towns and starts a gang war. which leads to the 5 nobles feuding. the dopplegangers could keep things moving along thru ever escalating violence, while the PC begin to suspect someone else is fuelling the fire. during slow parts have random city stuff. building accident, drunk warrior, pickpocket, duelist, robbers, etc.
several awesome city source books out there to help. cityscape, cityworks, the quarters series by game mechanics.[ theives quarter, priests quarter, etc.] the aristocrats handbook, and dynasties and demagogues also speak of political campaigns.
I'm currently listening to an actual-play podcast with a strong intrigue theme, you could try mining that for ideas (downfalldnd.wordpress.com).
Can't have a good city without a good Thieves Guild. Throw all the "seedy underworld" tropes at them, including the informant who's really a plant, feeding the party false information which leads them into a trap.
The neat thing about cities is you can use a broader range of source material for inspiration. Take practically any TV drama and retool it. Have rival gangs vying for territory a la Sons of Anarchy. Have solo criminals trying to make a buck like Breaking Bad. Throw in a creepy murder spree from X Files.
Good luck!
In my setting there are two rival thief guilds, and a third party that is trying to start a war between the two. The players prevent this from happening, and thus make allies out of them both. Now the thieves provide the players with information. They also discovered that the captain of the guards was really acting as a secret informant for one of the thieves guilds as well. As it turned out, the captain of the guards was allowing this sort of low level crime, in return for information regarding the real threats to the city.
-Then there are all sorts of noble houses, lots of gossip and nobles with secret love affairs.
-One of the close allies of the players is challenged to a duel by a nobleman, and now the players must resolve this fight some how.
-There's the slums outside the city, where a group of fanatical paladins are recruiting the poor for their faith.
-There's dwarven protests all over the city, because they believe the government is responsible for sinking one of their ships.
-There's a religious festival at some point in the city, with lots of games and drinking.
-There's of course the sewers, with various dark organisations making it their home.
-There's a church with a dark secret deep within it's catacombs.
-Then recently the ruler of the city was assassinated, so now the players have to work out a way to influence the nobles to vote for a particular new ruler.
Cities are a wealth for any campaign.
In a large port city, a conflict with the longshoremens union has a lot of potential for action and politics.
Any number of buildings can have any kind of giant vermin in the basement. For a quick fight, you can declare that a desired object - key, document, orb of power, secret tunnel, kidnapped child, witness in hiding, dropped contact lens, portal to oblivion - whatever they want, it's in the basement infested by giant vermin. It's a staple encounter in many games.
Any time the party wants to go from one area to the next, they have to walk the streets. Streets are always crawling with street gangs (a fight) and pickpockets (a skill encounter which can lead to a fight). I've also seen belligerent drunken warriors, and one encounter with an XP-crazed rival adventuring party.
On long treks across the entire ciity, you can have abandoned city blocks that are infested with monsters, effectively making them wilderness encounters with an urban backdrop.
For an unusual twist, introduce the practice of dueling. Make up whatever dueling rules you like; one-on-one, last man standing is pretty easy. Have npc's challenge specific party members rather than the entire party (otherwise the barbarian would fight all the duels). In the game I played, an npc had agreed to sell a map to the players for a few hundred gold, but then added that she would give the party free supplies if the party paladin beat her champion in single combat.
Then you have the superhero staple - people so powerful that they don't care whether anyone sees them fighting. They fight in the street and throw people through buildings, and only the heroes can do anything to stop them. Even though your players are more interested in political struggle, there are still ways to take down a classic bank-robbing super-villain through stealth and treachery.
Nothing beats a good chase scene through the crowded city streets. Just remember action does not equal combat. Every aspect of this game is action, the players must do something to overcome whatever obstacle that's in their way.
For intrigue, I always go back to Dumas’ Musketeers works. There’s plenty going on politically, but sometimes the velvet glove needs to hold a sword. The musketeers faced off both covertly and overtly against Richelieu’s forces.
I also agree with Frimbrial – just throw some monsters in the city. I’m currently doing an urban campaign, and was having trouble figuring out which monsters to use, until I decided the heck with it – if I want hobgoblin mercenaries lurking about and carrion crawlers prowling about, why not?
Wel with a council of 5 ruleing there might be a power struggle behind the scenes where some or all of the 5 are planing to become the sumpreme ruler.
Each counselor would have his own needs, wants and likes.
And recources to his/her disposal
Well, you could watch Game of Thrones for 5 seaons. 
In my opinion, create the five groups and build the personality for each head. Then build the subordinates.
Rome had the best political structure to look at, but then mideval Europe and early China also had great political struggles.
Remember, all rulers have someone they have to appease to keep their position. Mideval Europe had the church with its inquisition, Rome had the senate, China and Japan were based on the people and military rule.
Quick list:
Military
Trade groups
Senate
Churches
Land owners
Noble Families
Each one of these could use the party early on before you even get to the main political groups. No better political chaos than the famous infighting of a noble family. Look at the Scots and their self destructive royals.
So, who does each group have to appease? Could be something different for each. How do they plan to govern the city?
Also, try to break sterotypes with your NPC's. Evil people do not have to look evil and good people are not always beautiful.
Last thing, leaders do not like it when parties get more fame than them. You could do a whole bunch of stuff for one and he tries to destroy you to avoid your popularity.
Hope that helps.
You can't do it all the time, but... if you ever want to shake up a city?
Use a natural disaster. Cities can become utter liabilities during Earthquakes, tsunamis, tornadoes, hurricanes, etc.
If you have warning of one, you have the opportunity to prep the city for the oncoming disaster, during the disaster you need to save people, even after the disaster you may need to save more people because of the devastation left behind, then you need to work on rebuilding the city-- which means finding funds and materials and people with the skills to do the job.
And when the city is in its worse shape, you have both external enemies who will be looking to take advantage of the vulnerability of the city to invade or plunder or simply finish it off and drive the people out. And you have internal enemies, who will try to profit off the situation-- both in illegal ways and in technically legal ways, both monetarily and politically.
The thing about utilizing a natural disaster is that if you plan it badly, it could result in a short, boring scene that goes no where.
But, if you plan it out well and really think it through it could lead to a whole series of stories that keep you going for several sessions and that one local event could even become the centerpiece and driving factor for a good portion of the campaign.
Steal - excuse me, imitate - other peoples' work. Waterdeep: City of Splendors was a gold mine as I worked on my Tiamat group's campaign. About 1000 plot hooks cleverly disguised as a City Gazetteer.
Borrow it from your public library if you are a cheapskate and won't buy your own copy (like me).
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