I've been a bit lax in describing the growth progress of my cities. But you can see in that picture how fast my core cities have fully grown. Still even before the calendar change, Gaia's Landing and Song of Planet are sizes 19 and 18, while some of the other AI capitals visible in that screenshot are sizes 6 and 8 and Paris mighty at 11. In fact, I have a full five cities bigger than any AI city at all.
Well, okay, that goes a bit against the grain of SMAC's Gaians; green motifs in that game involve slowing and curbing population growth. (It's true in real life too - the best thing a person can do to minimize one's environmental impact is croak. Think about it. No more carbon emissions at all. But let's not dwell on that topic.)
Anyway, I've identified the three culture cities: Gaia's Landing, Song of Planet, and Chiron Preserve. The first two are no-brainers as my oldest and most mature cities. The last was my captured and renamed barbarian city. Despite its later start, it does seem the strongest option. It has nineteen forest tiles for hammer production, four deer for extra food, and a few hills and plains for extra hammers. Most other cities are missing some forest or hammer potential. Finally, Chiron Preserve is excellent as a culture candidate with no fewer than three rival cities within flip reach!
Song of Planet has been chosen as my primary Great Artist producer, since it's got the most food for specialists. It'll get the National Epic / National Park with a pure pool of Great Artist points, while my capital does other interesting wonders like the Hanging Gardens. To start racking up the culture, I'd built the Statue of Zeus, purely for its culture value and Great Artist points.
In the earlier days of Civ 4, I tended to dismiss great wonders for culture production, but that's really not true. An ancient wonder built early enough for timely doubling really does rack up some serious numbers. What turned my eye on to this was our Parthenon grab in the RBTS7 succession game. That city somehow became our cultural leader for most of the game, despite never having any Great Artists or major culture production besides that one wonder. (Unfortunately, the Parthenon is obsolete here thanks to Scientific Method. I'm compensating as best as I can.)
In the tech department, I traded for Monarchy, though had no need for the HR happiness just yet. HR is the favorite civic of three of our rivals, so I decided to wait until someone actually came asking for me to switch.
After Aesthetics, I started researching Drama, but then a rival came up with Calendar. I wavered on going for the Mausoleum, but it's so good: nice effect, +10 culture, and Great Artist points. The Dutch capital was only at size 5, with no marble, so I decided to have confidence in my size-18 city winning that race. I did win, though I got paranoid and whipped the wonder as soon as I could.
In the religion department, I took Judaism, sharing with Pericles (the founder), Louis, and Gilgamesh. Gilgamesh founded and switched to Confucianism, though. Then I noticed that Egypt didn't have much commitment to any religion, so I flooded Jewish missionaries that way and she converted. I think I had help - two Egyptian cities even got Judaism before my missionaries got there.
In a location that shall not be named, we had a discussion about early combined food and hammer production being the best indication of a civ's power.
Yeah. Although that won't last forever - most of the AIs have matched me in city count and land, so eventually their city sizes will catch up.
With all these forests, my building capacity started racing considerably ahead of my research capability. Every city built a Jewish Temple, in anticipation of exploiting the Sistine Chapel 1000-year doubling effect. They also easily built granaries, barracks, and a total (somewhat overdone) of 21 workers, and then enough archers and axemen to put me on top of the power graph.
I'm on my way up to Music now, with a lock on the free artist, and taking Literature on the way for the discount and to get the Heroic Epic up. It's going in Resplendent Oak, my next best hammer city after the legendaries.
Louis built the Apostolic Palace for Judaism, my religion - and I stole the election. I had enough population to do it all on my own, but even got support from Hatty and Pericles. I love sliding in that back door, picking up the hammer bonus for free on somebody else's investment on the tech and wonder.
Meanwhile, a couple wars broke out, but as long as I wasn't involved I didn't care.
The Music Great Artist along with my first natural one both settled in my late-starting city, which still needed a culture push just to secure control of its own radius. The very turn that I gained control of that tile, a French worker finished chopping its forest. 
Minus one forest preserve. But in a way, that's actually good; since I can road that square now, I finally get an overland trade route to Chiron Preserve rather than relying on that river that goes through Russian territory. Hopefully forest will regrow over it sometime.