I'm with the ICS / Dense build school of thought.
I build very dense cities , ensuring that each one will have access to 2 glassland or other 2 food producing tiles. I also try to use rivers and grab the real power tiles such as cattle, gold and whales. I try to visualise which towns will make good 12 pop cities, and which will just get in the way once I've grown. The "in the way" towns I give a name the ends in "Farm" so I remember not to develope them. If they are food heavy then they are just settler worker farms. If they seem to have enough production as well then I build a bararcks and use the to build units as well as worker / settlers. Eventually they will get abandoned, but often not until the local city builds a hospital. Often a city does not need a hospital. Core cites generally benefit with their low corruption, but ask yourself if a 60% corrupt city really needs to work 1 hills , 4 coast and 3 sea squares extra, and create pollution in the process.
A city with the Ironworks, the colossus or any of the science boosting wonders should realy be allowed acces to the best tiles it can reach, but often there is room for a farm in its radius until a few turns after it builds its hospital.
In the far reaches of the empire, as city is only there to control territory and resources. I build a temple, a wall, and a barracks. If the town looks like its going to be under cultural pressure I'll build a cathedral too. If the town is on an island and controls a resource I'll rush a harbor if I need the resource. I only rush the temple unless I expect combat in the area. Border towns are spaces so that the boder closes after one expansion ( ie 4 clear tiles apart) or sometimes further spaced. They are positioned on hills, besides rivers ( for defense), or actually _on_ the resorce they are there to control. If there are no more useful buildings to put in the border town the I set it building my best defensive unit at 1 shield per turn, eventually it completes.
Capital moving :
Your capital is generlaly in a bad place for a capital. Its on the coast, and you positioned it when you knew virtaully nothing about the map. The method I use is to rename the capital "Capital Farm" to remind you not to develope it, use it as a settler and worker farm. Once you have enough towns to build the Forbiden palace, build in close to the capital (this allows it to get build in a reasonable time as corruption is low) to be positioned to support your inital expansion lobe. You'll hav scouted the map by now, so choose an area to be your second core, with lots of good city sites in a roughly circualr area, then grow a city there ( it will be corrupt to hell ), get it to be the largest cisty in your mpire by mikling and other big town for settler s/ workers, then abandon your original "Capital Farm". You now have 2 productive cores to your empire with well chosen centres.