Spread out your inner cities a bit, Especially plan for 1 or two cities besides cap that can use most of its squares and will eventually really produce. But don't be afraid of overlap either.
I've placed cities with only a square space between them or 4 squares between em. It just depends. Just don't let good squares go to waste unless they are desert. (coast squares and their special resources are especially challenging to not let go to waste, but worth it sometimes)
Remember, if cities are 3 squares away then you can move a 1 move unit between them in a single turn, Useful for defensive fighting. Also overlapping squares means you can build up squares for several cities at once (when building settlers and workers)
Also its better for cities to be a bit closer if they are positioned kitty corner from one another.
Ok general rules of thumb, don't worry about 4 spacing much, hospitals are a long ways away from ancient. Even then you can just irrigate stuff and use specialists. You only "need" 1 or 2 or maybe 3 cities with all its squares (cap plus other cities not too far from cap, one of which should have your forbidden palace)
Not counting city square, 3 spacing left and right, top and bottom, 2 spacing when kitty corner.
But don't get too hung up on that. Place according to terrain. (trying to get fresh water and placing border cities near hostile nations on hills etc) Try not to let good squares like shield grassland go to waste.(where no cities cover them) remember you can compensate for cities being extra close on one side if you you give them extra space on the other side (like a city could have another city 1 or 2 squares from it on the left, just space city on right a bit further away)
Remember, bonus resources that produce commerce go through to the city on top of it. But shield and food bonuses are mostly lost. Which is why you dont want to place cities if you can help it on shield grass, or cows, or game or other such. but maybe on desert square if the alternative is a grass square or something. If the alternative is flood plain its a tough choice since then you get river bonus.(namely 12 without structure) Cities on top of gold just makes sense though.
Cities further away that start suffering real corruption should start to be even closer. Only time I might make these farther away from one another is if im trying to quickly expand to a resource before another nation can.(you can just put a city there but then its isolated)
). Which area of land / which resource to claim first, what to sacrifice to gain another advantage (things like fresh water, coastal access, access to powerful resources, etc.) Also, read up on city specialization in the War Academy so you'll know what places to look for for specific city types you're going to build. Sooner or later you'll be limited in the numer of cities you can afford, so it's good to make sure early you will have at least one each of a great production and a great commerce city, for example.
. I favour cramming a few extra cities into the spaces between my main cities. In the middle game (say 1000 AD) rather than have a few mediocre cities all with perfect fat crosses and a lot of wasted weak tiles (like plains or coastal) you can have more cities (perhaps twice as many) with quite a few overlapping fat crosses and all the wasted tiles able to be worked. The second case will be a much more powerful empire with a larger pop. It will have much higher maintenance costs for its many cities, and a larger civic cost (due to bigger pop) but the larger pop will also reduce the costs of the much larger army. Those higher costs will easily be offset by the fact that many more tiles are being worked, many cities will be at the happiness cap (determined by resources and technologies unless you run HR) or the health cap. There will be many more worked cottages and the main cities will be better developed.
