Population in 3.5: 23,192.
Population in 4E: intentionally vague.
I say intentionally vague because the Neverwinter campaign book clearly talks about a mass exodus and a progressive growth caused by the new wave of adventure, intrigue and commerce. It's hard to make a census when a big part of your city is lawless, in ruin or just a big hole in the ground. It is mentioned that "[the] catastrophe drastically depleted Neverwinter's population. A few dozen holdouts remained, refusing to leave their ancestral homes." A few is a vague and open amount (definitely more than a couple).
Recovering from a catastrophe like this takes time or at least a source of motivation. When the immediate area becomes safe again, people can come back and establish families again and the city can grow again. Apparently it is not totally the case yet. The city is a little bit of a mess. A quick look at the map, I'd say almost half of the map is in ruin. People are resilient and can live in ruins.
I'd say anything between 3000 and 5000 would be reasonable. A good slice of the population could be people who weren't born in Neverwinter but moved here because of opportunities like merchants, mercenaries, adventurers.