Some immediate thoughts:

“how would you play the bugout of B from Manhattan? Would she try to get off dodge by train, bus, boat, foot? Trains would be likely knocked off service by the power outage.”

How you get there is depends on where you are going, from the scenario, I assume the mountain location is on the west side of the Hudson River, so staying on that side of the river would be a good idea. Means of travel is open---the scenario does not give enough facts to decide, but I would assume a boat would be a good means, as that was the primary means of travel north from NYC in 18th Century New York State.

“which location would you choose for the meeting point between B, who is bugging out, and A, who is rushing south from Upstate to pick her up? Some place in New Jersey? Yonkers? Must be a place along a major route, but not so much that the flood of the evacuation compromises A&B chances of returning safely north by car.”

Depends on where they are located and the relative distances. No one answer without geographical facts and means of transport by both parties. You need both locations to figure out a good meeting point. New Jersey and Yonkers are out of the question. Look along the Hudson River. If its so bad as you describe, traveling by car may be out of question.

“Would the cell network continue to work after a widespread power outage, thanks to the backup generators of the towers? And if so, for how long do you expect them to keep working?”

It depends—author decides. I would assume no cell communications.

“Suppose you are A. You haven’t been able to communicate with B, by call or text, for some time now. You finally get to the meeting location and B doesn’t show up. Would you wait in place, or would you try to search for B further along the route she was supposed to follow?”

Wait for a while, but don’t go looking. B knows 2 places, where you were supposed to meet, and where the “safe” place is. Going looking, while dramatic, just lowers the chance of meeting up. Assume B if missing the meeting, will head for the ultimate destination.

I think it would be helpful if you sat down and did a study of a Google map of New York State. New York State is about half the size of Italy, so relative locations mean a lot---a great deal of territory to cover.