Okay, time for me to weigh in on this. I like a lot of the suggestions being bandied about here, and I've given this a lot of thought. Here we go:
Kyoto - Elizabeth
Beijing - FDR
Karakorum - Hatty
Delhi - Montezuma
(I went with FDR in China, because he's so regularly crapped on in this map that I'd like to give him a surefire powerhouse start. And Elizabeth will merely swap one island chain for another. I like Hattie in Mongolia and Monty in India for Jaaboo's reasons. Hattie might actually make real use of the steppe, and I'd love to see how the Aztecs do in a... target-rich environment)
Persepolis - Isabella
Mecca - Louis
Thebes - HC
Timbuktu - Frederick
Moscow - Caesar
(Putting the Incas on the Nile seems to be an obvious slam dunk. I wanted to put Isabella in a more central location where she can "breathe" a bit. It'll also be interesting to see how Louis does with access to a lot of marginal territory, as opposed to his usual gilded cage. And how will Julie fare in Catherine's spot? Freddy's usually a European power, so we're sending him off to languish a bit in Africa)
Athens - Tokugawa
Rome - Asoka
Berlin - Alexander
London - Catherine *
Paris - Saladin
Madrid - Genghis Khan
(I was originally thinking France for Tokugawa, but I like the suggestion for Greece. Really clog up the works and make a real obstacle between the East and West. Put the Mongols in Spain for easy access to horses and the possibility of a proper horde. Transform Alexander from European also-ran to European superpower. Give Saladin the ability to build the Mecca of his dreams, and save Asoka the trouble of having to cut back all that jungle. And we'll be playing as Catherine up there in the British Isles. The exact opposite of what Jaaboo wanted
)
Washington - Cyrus
Tenochtitlan - Mansa Musa
Cuzco - Qin Shi Huang
(I'd like to see how a pair of peaceful techers would do in the New World. Would they still end up as muddy savages, or could they build a utopia? Oh, and China will start in the Inca highlands because, well, eff Qin)
Oh, and re: America- I kind of considered the Sitting Bull game my homage to the American continent. Honestly, once Montezuma's wrestled to the ground, it ends up being much the same. It's a fair point, though. I also promised a Greece game way too long ago....