I don't know about World War II, but every carrier since the Forrestal has been built at one of three yards: New York Navy Yard in Brooklyn, Newport News Shipbuilding in Virginia, and New York Shipbuilding in Camden. Now we're down to Newport News.
Bremerton used to do overhauls and some construction, but nothing as large as a carrier.
Norfolk yard in a pinch possibly might be able to do it I'm not sure but it would take some major tooling up even for them and they do almost all east coast carrier overhauls except refueling nukes.
I've been at Portsmouth for an overhaul and it isn't a very plesant place. And I doubt that they have the workforce available anymore for major construction.
Me and a Deck Ape buddy had an apartment in Oceanview during overhaul. {Another place that is no more at least as most of us remember it being}. So we faired pretty good my last year in. I went on one three day shakedown about a week before I got out. I was taken off the watch list and was pretty much a trainer at that point. We only had one guy left in my shop that was there prior to overhaul that knew the equipment.