I have found, through trial and error, the best starting sites for cities for my style of play at the immortal level.
First, next to a river is important, but not essential.
Second, if this city is NOT your capital, your major concern is resoruces. I will settle on any site that commands 3 resources first over pretty much any other tile preference. Try to settle on a city that commands at least 2 resources if you can. If it is a resource you do not already have, then a one resource city is OK.
On higher levels of play (immortal, diety) SAFTEY is the primary concern. You should settle your first city close to your capital so that your defensive army can react to an attack on 2 fronts at one time (because it happens quite often in the early turns of the game.) You should still get at least one resource, that being said. On lower levels of play, this is not a problem, as I understand it.
When settling your capital, you are basically deciding if you will accept or reject the map the computer has generated. If you accept it, you start the game, if not, you start over and the computer regenerates the map. You may be so inclined to move a tile or two to settle on a hill. Settling on a hill is preferable becasue of the production boost, however, you will only get 2 hammers from the tile instead of the 3 that a mine would have given you. That is no problem if you have enough production tiles left over.
What tiles, in general, do you want in your capital? You want at least 2 tiles that will give you 3 or more food (2 farmed grassland would suffice.) Thats really all you need from a pure excess food tile standpoint early on. You then want to make sure you have at least 4 tiles that will yeild 3 or more hammers (those could be mined hills, plains horses with stable, grassland with stone, quarry, and stone works, or anything else that gives you 3 hammers.) Your goal early on is to get your capital to a pop of 5 with a production of 15. That will get your national college built in a reasonable time frame. I tend to stay at a pop of five in my capital for quite a while as my capital produces archers for defense and later to covert to crossbows.
In the early game, your capital will be producing the lions share of all your units. You don't need growth early on as much as units to fend off the AI and then to eventually conquer them. Thats why I will routinely reload a capital screen that gives me 4 resources but only one or two hills to build units with.
To summarize, riverside hills are your friend with building your capital, whereas resouces are what you crave for your satellite cities.
