I really hope you'll stick with the 1-tile cities. The proposed expansion tile that would indicate the cities specialization would be nice, or even gaining one tile every time the city levels. Both options allow you to make a clear visual distinction between different cities and city levels, and allow you to influence the shape somewhat. Which I'll grant can be pleasing aesthetically, and offers some strategy options. But only in moderation, expanding a level 2 town into hadrian's wall is neither imo.
The key considerations for going with 1-tile cities to me would be:
First and foremost, because to me it is the most noticeable. Where 1-tile cities make the world look huge, snaking makes it look small. Suddenly I'm no longer the immortal sovereign leading my nation to become the dominant empire in the world, but I'm the city zoning councillor, having to decide where each and every building is placed, for each and every city that I build or conquer. It turns forests into parks, mountains into hills, lakes into ponds, and continents into islands. It just changes the whole atmosphere of the game for me.
Snaking just kills strategy. With 1-tile cities you'll have carefully consider where to place your city. You would have to balance tile yield against location (next to the coast, near a river, in an exposed area or sheltered between two mountains, etc) and proximity of resource tiles (I'm not adverse to including these in the cities defence if placed next to the city hub). Where as with snaking, you just build the city on the best yield you can find, and then incorporate all resources into the city. A complete no-brainer. No need to keep an eye on vulnerable resources, there are none. You can defend them with the same stationary force as the city, and also have all the defence bonuses it has. There is no strategy involved in this process, only annoying busywork.
Those saying to use this method is a choice are wrong. A choice means that both options (snaking and auto-placement) have merritt. But one is clearly better than the other. If snaked cities were harder to defend (which they would be in real life), it would become a choice. But in fact snaking makes it easier to defend more stuff with the same force.
Right now there are only three types of player controlled structures on the map: 1) cities, 2) outposts, whose main purpose is giving access to 3) resource tiles. With on-map building, adding anything to this would just add more micromanagement and contribute to the cluttered look of the map. But 1-tile cities change the area around them into an actual province (rather than just room for expansion). Not only is this more interesting lore/immersion wise, but it also opens up space for a whole new type of player structures: improvements. I'm not proposing civ's covering of the map with structures. But what if you got to add 1 'satellite community' to the city for every city level? Some of the options could be:
Farming village: Adds the tile's grain yield (-1?) to it's parent city.
Logging camp: Adds the tile's production to the parent city.
Fishing village: build on river or coast, adds a fixed amount of food to the parent city, but at the cost of some production. This would be interesting for cities that are in rather infertile area's.
Town: Only gives 1 grain and 1 production to the parent, but produces ((grain yield-2)+(production-2)) in gold.
Breeders colony: Produces (grain yield/2) of the factions preferred type of mount.
Trade post: Can only be build on a tile where 2 roads cross, but adds 10% to the value of all trade routes on those roads.
I'm sure others can come up with more and more creative options.
To me, this would make the world and the game much more interesting.