I'm in a regent game using Egypt (just to fill you in).
I had a okay start, and when I started I did the circle pattern for my cities. From my capital, the first set of cities were all at 4.5 distance, and the second set all at 7.5 distance - in total I made ... gah 17 cities I think it was.
Corruption is based on distance the city is from the capital among other things. In my case, I have 6 cities all at the closest range to the capital (4.5 distance), and 10 at the outter ring (7.5 distance).
In addition, I built two other cities on the outskirt of the outter ring to grab horses and some silks - gotta keep the folks happy ya know.
Anyway, long story getting longer...
My first prioirty was to get my Pyramids up. So my first city built that in record time. After I start that in motion, I get my workers flowing out in masses along with my spearmen to survey the land and fortify at future city cites (I build these from cities 3 through 6 usually).
Okay so from city 7 (and 3 through 6 once I have enough spearmen), I start building my chariots in case I find a nearby civ.
In this case I didn't, but I did get a lot of goody huts giving me techs, how nice.
By the time I found the first civ, and subsequently got comms with the other civs and all their maps, I was a few turns away from Middle Ages. Thanks to an earlier golden age, I had a lot of cash and a lot of chariots to upgrade to knights, so I pressed for Chivalry next. As soon as I got it, I mass upgraded 50 or 60 knights, and went after the germans and their weak spearmen and swordsmen. In fact, I don't think they had a single horse, so I got to whipe them out easy. The reason?
Well their placement on the map was perfect for my second Metro area. As I was warring with them I was building up pikemen and settlers. I captured their cities, starved them, and got rid of them in favor of placing my own cities.
One REALLY nice thing was that I got a military leader during my war with the germans. In the middle of the war, I figure out where my second capital would be, settled, and hurried the FP (Forbidden Palace). Also as I was warring, I began my second placement of circle cities ... again 17 total but at 4.5 and 8.5 distances this time to give a little more room so they didn't have to share as many tiles.
In the end, I had 2 of these for a total of 34 cities, plus 2 for resources, plus 3 cities that bridged the two sets (gotta plan ahead and not let other civs settle on my upcoming railroads).
With all these cities, corruption and waste were incredibly low - To the point that now I just got Motorized Transp, and I'm building from nearly all 34 cities (the other 5 were perma set to wealth long ago). My build times are 2 to 3 turns in all cities - given I do have courthouse and police station in all cities, but still - without the FP and the circle placements, my corruption would be 500% what it is now per capita, easy.
Long story short ... plan ahead and be on the lookout for good city placement, and hope for a leader to rush that FP - HUGE HUGE time saver and your empire will grow fast!
I hope this helps (sorry it was so long).
I'll try to post screenshots of the huge map in it's current state to give you a better idea what I'm talking about. I hate to blow my own horn, but this is the first time I tried this placement, and I did a damn good job! haha
**Edit**
Warning: Image size is about 700KB.
I took some screenshots of my map and composited them together - couldn't see the city layout from just one screenshot. I then just used MS Paint to save as JPG and it still ended up large. But check it out if you have high speed internet, or the time to view an image of that size...
YAR's Map
in a city
