you knew it was coming 
Istanbul.
France!
NYC, baby.
London
London. History, grandeur, power, interest, culture, politics…it’s got the best of just about all of them. It’s certainly got its faults as a city, and any number of other cities might be better places to live, or more exciting, or more whatever. But in terms of ticking off as many boxes of sheer “greatness”, I’m not really sure what the competition is. Paris has the arts and culture, but doesn’t swing as hard on the world stage - ditto Berlin and Rome. Moscow is supposed to be a fantastic city, but seeing as how it’s the capital of a rapidly crumbling nation, I’m not sure it could count. Any of the Asian contenders (Tokyo, Beijing, Hong Kong, Seoul) seem too insular (though of course I have my Western blinders on that count). Other Anglosphere cities (Toronto, LA, Sydney, Chicago, Cape Town), feel too small and unstoried.
Which leaves New York, which a lot of people will probably nominate. I don’t see it. Yes, both cities have great art scenes, are financially very powerful, very multicultural, and both have a great vibe and a sense of place. But London has ten times the history, is politically more powerful and more interesting, is physically grander, is cleaner, safer (I think?), and - this is important - surrounded by far more interesting stuff. In London you’re a chunnel ride from another of the world’s greatest cities, and if you want to stay in the country you can hop over to Bath. The equivalents for New York are…Philly and Jersey?
I’ve lived in both (and live in NYC now) and for me there’s no comparison. The only thing New York has on London is 24 hour subways.
I’d have to go with NYC. It has a certain energy and personality that just screams world-class metropolis. It is the very model of a modern city. It’s drawn all sorts of walks of life to it, from the down and out, to the uber-rich and famous. It’s western culture in a bottle. It’s the brightest, neon pinprick on the face of the earth. It’s a world unto its own. It may not have the history of most european countries, but it certainly has an interesting one in the time it’s had. And my god, it’s got a ton of rats.
FYI for people interested in the topic, Wiki’s article on Global Cities is very interesting.
Houston, Texas, baby. It’s where it’s at!!
Did I start a trend?
For me it’s New York, no thought*, no question.
#2 would be Paris, #3 Tokyo, #4 London . . . any further down the list and I think I might have to start naming cities I haven’t been to, and that’s less fair.
*Actually I’ve thought about it a lot, which is why I don’t have to think about it now :).
Without a doubt, there’s no place that can match New York City, NY, USA 
London, it edges out NY since a) longer history, b) Capital of a global empire until semi-recently, c) dominates its home country, London accounts for a far larger chunk of Englands GDP and population then NY does for the US d) it has that stupid ferris wheel thing.
Another vote for New York City, although London is a close second.
New York City.
New York is Amber. It’s Tanelorn. It’s the one true city, of which all other cities are just pale shadows.
Paris, France
London, England
Shattuck, Oklahoma
New York, New York
gotta be Chicago
The lake, the music, the culture, the history, the crazy politics
The BEST !
London
Obviously I’m biased, living in London, but…
In a close fought battle between New York and London, I say London has the edge. They both compete pretty equally on business, accessibility, multiculturalism and the arts, but I believe London trumps New York on history and it’s position as a capital city. If you could merge New York and Washington, then New Workington would win.
I’ve never been to any of the cities listed. The closest I’ve been to a ‘great’ city is Chicago.
From what I know if it, maybe Shanghai. Give it 20-30 more years to clean up the environment and keep building the economy.