The first time the PC's know there is something odd is that they see no guardsmen. They may see individuals with guards, but no-one patrols the streets on a regular basis. Homes, blocks or entire wards might have guards, but not the city entire; guards are something people or groups of people pay for to watch over their stuff. They'll watch, somewhat bored, as a person loots a home right next to the one they are guarding.
There are no temples. When someone needs a priest for healing or counsel, they know where to find one. He might hang out at the local tavern, or preach at the nearest fountain square, or just have a small shop.
There is no real city organization; perhaps the only things clustered together are things that are either forced away from everything else (slaughterhouses, tanneries), or where a few like-minded individuals go together and built things that way because it was easier (a couple of bakers next to the millery down by the river).
Finding anything is almost impossible for strangers. It's just assumed you know who you need to deal with for various things.
There are no organized charities or orphanages. An orphan may well be taken in by someone who wants them. A bum might be fed by someone moved by his plight.
There is law of a sort, but there is no rule of law. The judges are not ruled by precedent or swayed by the wisdom of the past; they make judgements based on what they are told, what they know of the person brought before them, and what they feel like. Nothing is written down and each judge interprets things differently, according to his beliefs and predjudices. If you are found guilty of a crime, ther punishment is whatever the judge decides: usuaally exile or death, since either means no-one has to bother with you again.
That's assuming you get to see a judge. Transgresions are handled at a local level, either by individuals, people they hire, or by mod rule. "Thief!" brings out people who want to see a thief caught, or people who are friends or associates of the person yelling; the thief, if caught, is beaten by them - or whatever they feel like doing.
There is no government; there is rule by power group. Rulers are people who can attract and maintain followers. That's all. Some parts of the city might as well be different cities or nations, depending on how strong the individual power group is and how many people they can directly influence. Rulers are followed until they screw up or until they tick off a significant number of their followers. Keeping track of who is in and out of favor is a full-time task for some people.
In a way, it's rule-by-celebrity. An adventurer who comes in and slays a demon terrorizing a neighborhood suddenly is a mover and shaker in the government for that area as the residents try to please him so he does more things for them. He might could wine and dine for a few days but eventually he's going to have to do something useful or he's out of favor and no-one will provide him a place to live.
Economics are.. weird. Prices eventually will find some degree of equillibrium, but boom and bust is even more prevelant. Strangers from out of town will probably be fleeced of everything they have unless they prove to be entertaining or dangerous to cross. Merchants have no problem quoting the handsome bard one price and another, higher, price to the surly halfling. Haggling is the order of the day.