At one time we had Newport News {the only one left} , Brookyln, Bremerton, and I think Long Beach as all being carrier production capable. I know Brookyln or NYC built at least one I think it was the Kitty Hawk itself. We went from four {two on each coast to one} 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.
Rosie Roads had a Naval Air Station as well as a base. If I understand right the N.A.S. was closed as well. That part we could still use.
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.