Cities have souls. If humans, themselves collections of sinews, organs and tissues can have souls, surely so can cities with their streets, parks and electric grids. While different religions ascribe different properties to the soul of a man or woman, there are a few more standard proxies for measuring the soul of a city. They amount largely to two things, the strength of the neurosis that its citizens have about their city, and the percentage of people currently living in the city who are from said city.
Neurosis: There used to be a billboard (or so I am told) along I-95 that read "Philadelphia: it's not as bad as Philadelphians say it is." Residents with cities with souls have a neurotic obsession with their cities, an obsession with the identity of the city and how things get done there. It does not have to all be neurotic, New Orleans felt like a city suffering from collective post traumatic stress disorder when I was there, and San Franciscans seem to have an enormous amount of near narcissistic love for their city, seeing the city as the reflection of their own potential and ethos. While I may use psychological terms fast and loose, I do believe that these cities all actively acknowledge or wrestle with a sense of identity and what it means to be from that city.
Percentage of Natives: When someone asks you in Philadelphia or New Orleans, what school did you go to, they mean, what High School did you go to (not, like in Manhattan or DC, what college). This is not just evidence of a sort of parochialism, it is also a sign that natives have deep roots in these cities. Having a high percentage of people from the city, distributed across income brackets, means that people across the city have memories of the city. A friend of mine living in Albania, had an address that said "Mike, above where Disco-My-Heart used to be, Behind where the rice factory used to stand." While cities need immigrants and churn, new people moving in and out, for a city to have a soul, it needs people who remember what used to be on that corner a decade a go.
I often flippantly say that DC has no soul, so many people move in and move out so quickly in that City that its neighborhoods are forgotten and without identity. My friends who are from DC argue with me, noting that such a characterization is only applicable for NW DC, a white capital-hill-centric DC. I would be willing to concede some of that, but if half the city does not pay attention to itself, well I still think its souless. Manhattan too, it could be argued, is loosing its soul as it becomes more and more expensive and more and more out-of-towners live their and have lost the memory of a grimier and livelier past.
Some of this may sound like simple urban romanticism, but in the end successful cities are those that encourage people to live in them and raise their children in them. Not all these cities are functional, but they do have people passionately fighting for, well, their souls.