For career progression being at headquarters is always better. Better visibility, better high impact projects and etc. for dating NYC of course. But dating is only a problem in bay area if you are Indian. Otherwise you would do just fine. NYC has more variety of girls, open to dating any ethnicity
Not on your list, but the Chicago office is great. Chicago is very affordable and you still do very well from a TC perspective. We always rate as one of the happiest offices. It's a bit smaller than the three you listed, but there's an actual community. Pretty of PAs and career opportunities here as well.
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That's the definition of open minded.