John Wyndham's The Chrysalids is set in
post-nuclear Newfoundland.
The people of Labrador are described as venturing out along the coast.
Is there anything that gives us a hint how far down the coast they went?
Do we have descriptions of what NYC is supposed to resemble?
It's strongly hinted at that the more adventurous crews reach Central America and the Caribbean, possibly even South America.
As David's uncle Axel relates:
And yet it can't always have been like that because there was one ship whose captain was foolhardy enough to sail close inshore. Her crew were able to make out great stone ruins. They were all agreed that they were far too regular to be natural, and they thought they might be the remains of one of the Old People's cities. But nobody knows any more about them. Most of the men in that ship wasted away and died, and the rest were never the same afterwards, so no other ship has risked keeping close in.
For hundreds of miles the coast goes on being Badlands with stretches of the dead, black lands; so far, in fact, that the first ships down there gave up and turned about because they thought they would never reach any place where they could water and provision. They came back saying that they thought it must go on like that to the ends of the earth.
(...)
In the middle of all the fuss, however, a ship called the Venture which had long been given up for lost, came sailing home to Rigo. She was battered and undermanned, her canvas was patched, her mizzen jury-rigged, and her condition foul, but she triumphantly claimed the honour of being the first to reach the lands beyond the Black Coasts. She brought back a number of objects including gold and silver and copper ornaments, and a cargo of spices to prove it. The evidence had to be accepted, but there was a lot of trouble over the spices, for there was no means of telling whether they were deviational, or the product of a pure strain. Strict churchgoers refused to touch them for fear they might be tainted; other people preferred to believe that they were the kind of spices referred to in the Bible. Whatever they were, they are profitable enough now for ships to sail south in search of them.
(...)
You'll find islands where the people are all thickset, and others where they're thin; there are even said to be some islands where both the men and women would be passed as true images if it weren't that some strange deviation has turned them all completely black -- though even that's easier to believe than the one about a race of Deviations that has dwindled to two feet high, grown fur and a tail, and taken to living in trees.
The Chrysalids, chapter 6.
The islands where people are "all completely black" might be some of the Caribbean islands. How uncle Axel describes them, they seem to be at the furthest edges of where the Labradorian ships have sailed. The spices these ships brought back can easily have come from Caribbean or Central American countries.
Ships that come (too) close to the coast, see "great stone ruins" the ruins of cities, thought to be "the remains of one of the Old People's cities". So while there's no specific description of New York City, it's safe to assume it lays in ruins.
The "race of Deviations that has dwindled to two feet high, grown fur and a tail, and taken to living in trees" sounds like an accurate description of new world monkeys, found in Central and South America.
They seems to be regular travel about as far south as Nova Scotia. Some explorers have traveled farther south (to the US West Coast and even to South America. possibly) where they've witnessed glowing stubs of cities and experienced radiation poisoning along the "Black Coasts".
The implication seems to be that New York and the western coastal cities were almost totally obliterated in a nuclear holocaust.
The Black Coasts would appear to be an extreme form of Badlands. Since any close approach to them is likely to be fatal nothing can be said of them with certainty but that they are entirely barren, and in some regions are known to glow dimly on a dark night.
and
‘Uncle Axel, are there any cities there?’
‘Cities?’ he repeated. ‘Well, here and there you’ll find a town, of a kind. As big as Kentak, maybe, but built differently.’
‘No,’ I told him. ‘I mean big places.’ I described the city in my dream, but without telling him it was a dream.
He looked at me oddly. ‘No, I never heard of any place like that,’ he told me. ‘Farther on, perhaps. Farther than you went?’ I suggested.
He shook his head. ‘You can’t go farther on. The sea gets full of weed. Masses of weed with stems like cables. A ship can’t make her way through it, and it’s trouble enough to get clear of it once you get in it at all.’
and
‘This is a dreadful country indeed. We have seen Badlands before, but none of us has ever imagined anything quite so terrible as this. There are stretches, miles across, where it looks as if all the ground has been fused into black glass; there is nothing else, nothing but the glass like a frozen ocean of ink… then belts of Badlands… then another wilderness of black glass. It goes on and on… What did they do here? What can they have done to create such a frightful place?… No wonder none of us ever came this way before. It’s like going over the rim of the world, into the outskirts of hell… it must be utterly beyond hope, barred to any kind of life for ever and ever… But why? – why? – why?… There was the power of gods in the hands of children, we know: but were they mad children, all of them quite mad?… The mountains are cinders and the plains are black glass – still, after centuries!… It is so dreary… dreary… a monstrous madness… It is frightening to think that a whole race could go insane…. If we did not know that you are on the other side of it we should have turned back and fled—’
Past the Badlands, as SQB has noted in his answer are areas where there are people with black skin and what appear to be primates. It's not clear whether this is South America or Southern America or the Caribbean but it's described as being found after "hundreds of miles" of blackened coastline.
For hundreds of miles the coast goes on being Badlands with stretches of the dead, black lands; so far, in fact, that the first ships down there gave up and turned about because they thought they would never reach any place where they could water and provision. They came back saying that they thought it must go on like that to the ends of the earth.
