I've experienced the opposite too, having lived in both NYC and San Francisco: urban homogeneity, and even monocultures.
Yes, San Francisco is very diverse in the origin of its people, but the people who move there tend to fit certain molds, regardless of their cultural background. New York might attract more varied "types", but the act of moving to NYC still tends to select for a certain socio-economic level, a willingness to make certain sacrifices, people with certain life-goals and expectations, etc.
I surprisingly have found more diverse personalities and ideas in smaller places that are less selective (in price, profession, ideology, etc) to move to or to live in. Places where a software engineer might frequent the same gym as an insurance salesperson, an elementary-school teacher and a tattoo artist, even if (and perhaps because) they're all from there and didn't move in for a job.