Do not Overthink the City
Have you ever lived in a city? Think back and you will notice: your experience was mainly a series of rooms. You visited perhaps 6-12 rooms each day. (Usually the same rooms everyday). Maybe more, if you're out and about. Sometimes it was park or a square. Those are just rooms without walls. Alleys are rooms with 2-3 walls. The number "rooms" depends a little on what you count as a room. Any place you had to stop and wait or do an activity is a fair definition of a note-worthy room.
I remember my old cycle of rooms in NYC perfectly. Studio apartment, subway stop, subway car, lobby, production line, corner bodega, then do it in reverse. If my daily life were a game, those rooms were really all you needed to key.
The secret, I posit, to writing a good city is to just write really good rooms. Interesting ones, with stuff to do and play with.
Factions, politics, institutions, NPCs - all good interesting stuff. Where are they? The damn rooms. Put that stuff in an interesting room.1
You could leave the rooms as notional things until players arrive at the doorstep. "Kitchen," "docks," "apartment." This is a fine solution if your players barge into some formerly unimportant room. But it misses the joy and intrigue of a city: precisely the intricate, living infrastructure of the city. Don't deny the players the opportunity to run around a richly realized warehouse, construction site, or penthouse.
How many rooms? However long the adventure is. 6 is a short romp, done before dinner. 20 is a medium sized challenge that may unfold over 1-3 days. 100 is a mega undertaking; you'll be here for for a while. In this respect, the scope of a city adventure is similar to a dungeon. Many of the same principals will apply. Consider your city adventure as a dungeon chopped up and spread over a few square miles.2
And Yet the City is not a Dungeon
There are two considerations unique to the City: navigation and the latent potential energy of the unseen portions of the city. These are significant, but only a small amount of attention need be paid by the GM to produce an adequate effect.
1: Navigation
Instead of halls between rooms you have directions. When the PCs first arrive in the city, they need the "entrance." That is, either they already have directions to the first room(s), or they know whom to ask, or where to listen for rumors.
If you keep your city adventure isomorphic to a dungeon's structure, then directions to new rooms will have to be obtained within rooms, essentially creating a point crawl (though back tracking can be done from any 2 nodes). There's nothing wrong with that at all. It Will Work.
However, even a simple list of known addresses which is occasionally updated is functional. Simple as.
A higher effort option looks like Citizen Playbooks.
For my money, a modified Flux Space procedure has a lot of promise. (Example forthcoming, when I finally get around to making good on my Villian26 post).
What of Traversal?
Instead of walking down halls, we've got following the directions. This is usually simple and boring, and you should skip it. There's no need for dungeon turn procedures here.
A rare streetside happening or getting lost wouldn't go amiss, but tune the frequency way down. Walking from A to B in a city is usually just that, walking.3
2: The Teeming Peoples
Tens of thousands, or even millions of individuals. Each plotting their own petty hustle or plodding along a quotidian grind. Neither interests us, except for the potential to intrude on our keyed rooms.
In a city, usually the only people supposed to be in a room are present. So any such NPC's should be in the room key.
Interlopers
However, your city will feel alive if there is a chance interlopers can appear shortly prior to or during a PC's visit. Spend energy on this before any streetside events.
These can be short table of random complications with a low chance of occurrence. Just try to give an sampler of the interesting sorts of denizens who didn't make it into a room key. Depending on where they show up, you'll have to decide if the interloper is invited, uninvited, or trespassing. Hopefully it is obvious based on the room and the person.
One table of interlopers demonstrates to the players that in a city all sorts rub elbows. If you need more detail, different neighborhoods can use their own table. (And that's about the amount of effort that I think is worthwhile to spend on a neighborhood untethered to a room key).4
Other non-random intrusions should be left to the realm of fronts and faction dynamics. Elmcat has you covered there. There is nothing special about the city in this regard.5 The city is just another arena for the powerful to duke it out.
What about the Big City Sandbox?
Hopefully, it is clear that a city sandbox should function similarly to a hexcrawl sandbox. Just as you'd sprinkle dungeons over the region, you do the same for the City. On the macro scale, they all fall on top of each other. On the micro scale, the rooms of each dungeon are scattered about. No matter, batch and conceptualize each "city dungeon" as its own little adventure following the principals above.
Prioritize your sandbox elements to efficiently prep them. Instead of using distance as a limiter, you'll have to use time or PC knowledge. Some city adventures will only present themselves to the party after some number of days (or faction turns) or until PCs acquire certain rumors or contacts. I acknowledge that this is a little less intuitive than marching on a map and seeing what is literally nearby the PC's.6
When it comes to the non-adventure stuff that stitches the sandbox experience together, you already know how to do this. Rent beds, go to merchants, carouse. Nothing about this fundamentally changes if you're doing it in between outdoor expeditions vs. hitting the bricks in the city.
Don't overthink it.
To have fun in a city, there needs only be an adventure in the city. The adventure will take place not in abstract spaces, but in specific places -rooms- which heighten and facilitate the play experience. Cities have people, some of whom are important NPCs. Put the important NPCs in the rooms as well.
If you want to get fancy, let NPCs change rooms, coming, going and disappearing on their own schedule. But if it follows the logic of work day, it is probably unnecessary to write down.↩
E.g. Write rooms in pairs, or patches. Use checklists. Make encounters sticky. The vast majority of these advices and the many more like them still spend. A "dungeon" more focused on exploration over homicide would probably also help. A traditional wandering encounter table is probably unnecessary unless a consistent mix of folks traipse to and from these specific rooms for some reason. But read on to my section on interlopers for a similar idea.↩
Maybe if you're going to the bad part of town at night roll for an encounter or something. Luckily every aspiring city adventure can modify any number of x-crawl procedures for traversal complications. In a pinch, AD&D has you covered (But watch out for that harlot table, oof).↩
I often see the advice to key specific districts or neighborhoods, and I seriously question this advice. It is neat if the GM narrates the streets of the slums different to uptown, sure. They could have differing streetside encounters, sure. But as I discussed, the meat of the adventure is going to be in the rooms, not randos accosting the PCs as they walk about. It's better to reflect the neighborhood environment into the key rooms and their occupants. If the character of neighborhoods is really something you want to explore, I would assign whole dungeon patches or adventures to each neighborhood.↩
Weeeeell, if your city has something like a police force, then tracking their faction is probably uniquely important. Adventures tend to have developing illegal situations that ought to attract cop-types. So there's one special thing about cities. The more shenanigans the PC's get entangled with, the more likely it should be that a cop shows up as a room interloper.↩
Consider this: Nothing is stopping you from using hex gridded paper behind the screen. A kind of hex-mind-map to see how far players conceptually are from one adventure or another. In this framework, the points of interest on the hex map could actually move closer or farther away from the PCs independently as time and faction turns tick by. That'd be a funky little GM minigame!↩