Moved over East one or two spaces for first city (you can tell where to go because of the resources) to grant water access, took advantage of Mysticism to get first early religion, which spread to rest of Europe except Russia and Greece as Arabs founded other early religion. Actually sent a few missionaries to ensure the religion stuck as Hinduism was beginning to spread and I was afraid Italy and Germany would flip on me, so I converted a few of their secondary cities. Generally tried to keep good relations with other local powers with trade and open borders, and out of their wars.
Built an early galley and founded second city in about Tunisia to make sure Rome or Egypt didn't move there, and then third city right where Atlantic and Mediterranian Sea meet (which recaptured a resource or two I lost in Iberia by moving Madrid east). Then I just put some emphasis on culture buildings to keep the borders stable, built up a modest deterrent defense, sent a missionary to Mansa who was still without religion to keep him peaceful, and got some good tech trades from Mansa as well.
During this time, I was peaceful with my neighbors. I did get war declared once by Mongolia for some odd reason who managed to actually get a stack to Madrid through open borders which my archers handled nicely, and once by Persia who never attacked. (This was the scary part, as Persia was by far the leader, with an empire stretching from Siberia to Vietnam, but Persia was in more or less perma-war with Russia, China and India so it never had a chance to attack me.) There were various unimportant wars in the area, the only notable one being Russia taking Paris and eliminating the French, the only elimination the entire game. My little three city empire was fairly competitive in tech and my overall was just enough to put me in the top third.
I didn't completely beeline it, but I did reach Astronomy well before everyone else, so I was able to implement my strategy from the beginning: South American Dominance!
My earlier caravel and explorer (I got the first caravel too, and of course circumnavigation bonus thereafter) confirmed what almost always happens: Monty preoccupied with Washington and the Incas too dumb to build a galley and put a settler on it to escape their mountainous prison. The bulk of South America, with its breathtaking river run plains, hilly resource filled coasts, and poorly defended but semi-developed and well placed barbarian cities was completely up for grabs. Isabella wasn't intimidated by all that jungle of course, being Expansive, knowing that clearing it and jungly health issues wouldn't be too bad.
Long story short, during the midgame I built enough of a galleon navy to protect my intercontinental shipping lanes and move troops about, an army to conquer the three barb cities, enough settlers to build cities to seal off the coast from Argentina to Panama (starting from the point of land in Brazil closest to Europe and spreading from there), and then had my new cities spawn enough settlers and workers to claim the Amazon basin all the way to the Andes. I wasn't quick enough to expand over the whole continent to stop Mansa from establishing a city on the southern tip and also the Faulkland Islands, but he was a middling power and my closest friend so I didn't get anal about it.
As I was establishing and developing my South American empire, China became the sole true superpower, with Mongolian and Japanese vassals (both five or six city powers in themselves) and a bunch of cities where you would expect. Persia was also strong, with a wedge up to the arctic between Russia and Mongolia and pushing India almost completely out of Asia mainland but for two cities, although India was still respectable in size if not development by being the one to claim most of Indonesia and Australia. Russia was in good shape, having taken a lot of Germany, Scandinavia, and Siberia until it hit Persia, as well as Paris as I mentioned earlier, although Germany still had two cities. England had a few colonies in the tundra area of Canada, one in Cuba and also two in South Africa, so was respectable. Egypt had most of East Africa and the Mideast, leaving the Arabs with just two cities in Arabian penninsula. Mansa was average in West Africa. Rome and Greece were both two city powers, eventually vassalled to Russia and Persia respectably. No one in the old world paid much attention to me, although I did pay out some tech bribes from time to time to keep it that way.
Halfway through settling South America, Monty made America and the Incas his vassals and of course declared war on me. However, through naval dominance and the fact that a mountain separates North and South America, this wasn't a problem. I just kept sinking his ships. He did land a couple of invasion forces on the northern part of South America but I was able to beat them back. We went back and forth between war and peace until the end of the game. I was tempted to take the three cities of his Incan vassal because Incan culture was impeding on my Amazon cities, and probably should have just for the aesthetic value of owning the continent save for Mansa's two cities in the south, but didn't because by then I was well on my way to winning.
Winning via space, of course. I had kept my research high throughout and built all the research buildings wherever reasonable, wasn't wasting many resources on military beyond basic city defense (and a fairly large army in Madrid with transports to take them to my two North African cities if necessary, and a big army in South America just in case), wasn't building much of an economic base beyond a gold city in South America, and wasn't paying attention to espionage at all.
Once I got Apollo, I had three monster production cities ready to build what I needed (two in South America, both former barb cities, the other in North Africa which I had earlier given Maori). It was all she wrote from there!
This game was fun because it didn't rely on the usual crush your Western European neighbors strategy and glide to the win. I got pretty lucky avoiding ruinous war early on, the mid game rush to fill out South America before anyone else gets there is fun and takes some strategy, and it felt great to stuff it in China and Persia's face at the very end when they were leading the whole game and to beat them without a shot ever fired.
The South American strategy works well for a bunch of countries but probably the best with Spain. Expansive is a big help clearing out the jungle, and with Spain you don't have to worry about the lack of open borders shutting down sea lanes once you get Astronomy to exploit it (Rome or Greece might be boxed in by a Spain which refuses to grant open borders for example; same with Germany being cut off by England). Mali would work great too, maybe even better. And of course if you play the Incas, do what computer Incas never seem to do, build a galley early and claim the continent for yourself before anyone else discovers Astronomy.