If you're mobile and like to walk, try getting a cab over to the Piraeus metro stop. Then you can get into and out of Athens quickly.

But, you might have trouble finding a cab that will take you there, since it's a short distance and not much of a fare. In fact finding a cab to come back would be even worse; we had great problems finding a cab to take us from the Piraeus ferry port into Athens after a trip to an island (we were chickens, didn't take the subway, but we had luggage.)

I believe the subway stop is about a 15 or 20 minute walk, but Athens can be pretty hot in summer, and you'll do lots of walking once in town. So getting a cab straight to Athens might be best in the long run, but remember traffic can be pretty bad, so give yourself lots of time to get back to the ship.