Korvosa basically has 7 districts, plus 2 bits that aren't exactly part of the city but are getting swallowed up.
Quick rundown:
The Heights: snob central. Wealth and power (temple of Abadar, palace, castle) are concentrated here. Very well-to-do, heavily patrolled by the Korvosan Guard.
North Point: the bit that keeps the rest of Korvosa going. Middle class, industrious, where the traders and shopkeepers and professionals live. Quiet, very little trouble other than the occasional gangs.
Midland: the bit that does the work. Full of slum tenements and labourers, docks and wharfs, warehouses. Also home to Citadel Volshyenek, headquarters of the Korvosan Guard. Just as well, since gang and criminal activity is pretty widespread.
Gray: mostly quiet - the cathedral of Pharasma is here, as are the city's burial grounds and occasional restless undead (hence, 'mostly quiet').
South Shore: if you live here, it's because you think that The Heights are becoming too full of riff-raff. This is where the serious nobility live. Don't even think of walking down these streets if you aren't dressed for it.
Old Korvosa: basically a no-go area if you don't belong. Slum central, along with some very old nobility - the sort that make their own law and don't worry about getting caught, if you get my drift. The Guard come here as little as they can reasonably get away with - and in large groups.
East Shore: like Midland, only even poorer since it's further from the city centre. Gangs everywhere.
Thief Camp: no dwellings are allowed by law this close to the road, so it's a wash of squatters' tents and makeshift lean-tos. The Guard periodically come by and disperse it, but it always rebuilds. The name Thief Camp basically speaks for itself - if you're looking for someone disreputable you can find 'em here. Or someone who knows 'em.
Trail's End: a Varisian community of people who can't afford rent in the city proper. Basically law-abiding, if a little rough. The local gangs are Sczarni so there's some sort of honor code.
