Carrier hit...
A sub wouldn't be a practical or worthwhile target..small and hard to hit. Bin Laden was many things, but stupid wasn't one of them, so I'm going to look at carriers.
An underway carrier is NOT a viable target. They have rules of engagement that would allow them to shred a kamikaze before it hit--and the terrorists would presumable know that. Additionally, the pilots of the hijacked planes are NOT experts by any means. Once again, Bin Laden rules that out.
That leaves a carrier in port...that has possibilities, but also problems. Here's the problems as I see them:
Target selection:
9/11 required very good weather, and hence, was subject to postponement. Unless the ship was docked for an extended time, it's likely to move if there's a delay. Target gone.
For that matter, how good would the terrorist's intelligence concerning ship movements be? It's easy to see when a ship is in port--but not so easy to know when it WILL be in port, unless it's undergoing serious work.
Hitting the target:
I'll grant the terrorists the ability to crash dive onto a carrier in port. But within a half hour, I doubt that a second plane would be able to pull it off, at least on an active ship. Everything the US Navy has would be at battle stations, with AA weapons manned and armed. Even in a port where the carrier is stripped down for rebuilding, there's other ships that can man battle stations.
I think (but am not sure) that the decision to shoot down the plane attacking could be made, in this case, but the ship's captain, as his command is under direct attack. Defending one's own command against direct attack usually doesn't need clearance from higher up.
The way to get around this might be for every plane with a carrier available to have the carrier as one possible target, with a secondary target to be attacked once a carrier is attacked.
Damage:
The damage that the strike could inflict is, to me, the most difficult thing to assess. Carriers have LOTS of flammables aboard, and the ship is not at battle stations, but as open as a ship gets under normal conditions. The burning fuel from the jet could end up in some very bad places. The magazines are safe, though. There will be very few planes aboard; air groups fly off when a carrier will be in port for an extended time. This could be far worse than the fire on the USS Forestall back in Vietnam. This would, IMVHO, be unlikely to sink the carrier, but she might be a constructive total loss, depending on how bad it gets. Is the flight deck fire suppression system good enough to do the job? And even more important, the hangar deck system!
How much of the burning fuel would end up below, and how much would run off the flight deck into the water. Depending on the angle of impact, the wings (where most of the fuel is) might not even end up on the carrier, but in the water or on the adjacent dock, in which case the damage is much less.
Worst case: A carrier is making a short visit to a major city, but only for a few days, so the air group isn't flown off. A lot of burning fuel ends up on the flight deck, and starts a chain reaction of burning, exploding aircraft. The ship isn't at battle stations, of course, so damage control takes a moment to get going. Damage control would be a formidable task, with the sheer scale of the conflagration, and the total surprise. The ship possibly could be a total write off--though once again, IMVHO, it's unlikely to SINK.
Wrecking a carrier would be a major hit to the USN, but "heavy damage" doesn't look as dramatic to the world as a falling skyscraper, and lacks the CIVILIAN body count. It also won't do the same damage to the command and control of the US Military that a more effective strike on the pentagon has the potential to do.
In short, a strike to take out a lat of the American carrier fleet seems implausible, though striking one might be. The ship hit would be out of action for months to years, or perhaps permanently.
USS Independence was in mothballs, and could be returned to duty if need be; Saratoga and Forrestall were stripped hulks, that could, at massive expense, be put back into service. Constellation likely gets an extension on her career until the damaged carrier is back in service.
In short, one carrier severely damaged, or even wrecked, won't likely be as damaging as hitting one of the trade towers, but might be doable.