"Successful cities" is not an anomaly. The successful cities are the ones that really are cities. They have rail transit, are walkable, and they're relatively free of urban-fabric-shedding parking lots.NYC...and all of the other successful cities in the US (SF, Boston, DC, Chicago, etc).
I don't think New York is an anomaly. Successful cities may be an anomaly, but I'm seeing the same increase in families in other cities that I see in NYC.
van mentioned Buffalo and Indianapolis. Would anyone interested in urban living choose to move to such places for the urban vibe? Those aren't cities.
You can add Atlanta, Denver and Phoenix to your list. These places are gaining population, but it's for economic reasons, not urban enthusiasm.
The only bigger North American cities that can be regarded as having urban characteristics are: NYC, BOS, SFO, PHL, CHI, WAS, MTL, TOR, VCR.
Chauvinistically I omitted Mexico, also in North America. I know Mexico is full of cities, but this gringo can't compile a meaningful list of them without more effort than he's presently willing to expend.