[wat10000]

I checked and it seems like the reason for San Antonio was a mix of your view and mine (assuming we can believe the narrator here):

“At that time I got a look at the condition of San Antonio. I remember being astonished that this little city had been so terribly devastated on Warday. People had hardly even heard of it in Britain. One would have expected Los Angeles or even Houston before San Antonio. Of course, it has since come out that a good part of the planned Soviet attack didn't go off, so in a sense San Antonio was simply unlucky. The Soviets had given it first-strike priority because of the extensive U.S. Air Force repair and refitting facilities there, and the huge complex of military hospitals, the atomic supplies dump at Medina Base, and the presence of a mechanized army that could have been used to preserve order across the whole of the Southwest as well as seal the Mexican border.”

So the first strike was those three cities, and then the followup total strike didn’t happen, presumably stopped by the US counterstrike.

For Manhattan, it says that the biggest hazard is from chemical pollution from abandoned storage facilities, particularly nearby in New Jersey. Which seems kind of plausible, although I imagine people would be a lot more tolerant of such health hazards in this world. I guess everyone evacuated, and then the fact that you can’t just walk back to Manhattan might keep people from returning.