Maybe New York is the only real world-class city in the US. It's not a hard argument to support...
But, yes, if that's the definition, only New York (Manhattan in particular) really qualifies in the US. You can get away with it in other US cities but it tends to depend on stage in life, income, specific situation with respect to job etc., recreational activities, and how much hassle you're willing to put up with.
That said, living in Manhattan is a very specific lifestyle choice that isn't for everyone. I like visiting it now and then but the summer I worked there was enough.
"Tokyo has the lowest number in the nation–0.46 cars per household" -- http://blogs.wsj.com/japanrealtime/2014/08/18/number-of-cars...
I can't find cars per household for Paris, but cars per adult appears to be around 0.5, (https://halshs.archives-ouvertes.fr/hal-01069997/document), so cars per household can't be lower than that.
Hong Kong appears to be truly virtually carless.
In SF it's almost $12: http://yellowcabsf.com/service/cab-fares/
If we scale that to a 10-mile trip, assuming no waiting or traffic, which with SF is $33/hr extra, and in HK it's no charge (just by mileage) IIRC (having them wait is ~$12.38/hr):
SF: ~$31.05 HK: 150HKD=$19.35
This combined with their seriously great subway system ( https://en.m.wikipedia.org/wiki/MTR ) make it very practical to not own a car. You take the subway for short and medium trips, and hop in a cab at the end to get out to a relative's house in the middle of nowhere.
And Hong Kong is relatively expensive. My experience in southeast Asia is that, in some places, you can hire a car and driver for the day for maybe $50 or so. So--combined with how horrible driving in the big cities there are--many people just have drivers.
That said, there are very few US cities where you could live without a car without it being a hassle, especially if you want to leave your core urban area on a regular basis.