Of course the plot must be logical, even in fiction.
Stephen King's book Misery talks about this. You may be familiar with the plot--a writer crashes his car in a remote area and is taken in by a crazy killer nurse who is his Number One Fan and forces him to write a book to bring back to life his main character, whom the crazy nurse loved and the writer killed off.
At first the writer figures she's not that discerning a reader and will be happy with anything, and he writes some crazy melodramatic comes-back-to-life story. Annie (the crazy nurse) reads it and says, "No, this won't do. You're cheating." She explains that when she was a child, she went to see the weekly serial at the Saturday movie matinee, and one week the hero's car had plunged off a cliff and burst into flames. All week she wondered and worried about the hero, and hurried back the next week to see what had happened. It turned out he had jumped out of the car before it plunged off the cliff. But they hadn't shown that, and she felt cheated. She said sloppy plotting was cheating. She made him rewrite it and make it good and not cheating.
Misery is a great book. It's not just a horror novel--it's about the writer's muse. Seriously!
That being said, I agree that NYC would be an odd place to go after a nuclear war--it seems like it would be one of the most devastated places. Out in Montana or something makes more sense.