Arrival in Piraeus, then overnight before flying out of ATH

Are you spending any time in Athens?

If not I would recommend staying in Athens the night before your flight and take any of the public transportation available depending on your budget and convenience.

Metro is OK if you are aware of what's involved, so is a bus.

Otherwise booked a transfer with one of the other transfer services available which are more reliable.

Yes, we'll have a couple of days in Athens on the front end. Is there a spot in central Athens that's particularly well positioned for getting to the airport? I think I've read that there's a direct metro line from Syntagma Square, but is that equally convenient if we do a car transfer instead?

We have been using a transfer service in Athens since we were pick pocketed on the Metro a few years ago. They operate from Piraeus and the airport for pick up and transfer to central Athens. On one occasion we had an early flight and ordered a transfer for 5am. The driver was waiting for us at 4:45. We use City Cab but there are others like welcome pickups that provide a similar service.

Would you recommend simply staying in central Athens for the night and
taking a taxi or metro to the airport the following day?

Of course, Rafina is possibly an option only if your ferry departs/arrives at Rafina port. Yours arrives in Piraeus.

Taxi or metro, it's up to you to choose and it mainly depends on where your hotel is located. If it is a few meters from a metro station it could be interesting. Note that there are two metro lines at the port of Piraeus, the blue and the green. The ticket costs €1.20.

Also note that if you arrive from Cyclades with a SeaJets ferry you will disembark at gate E9 which is about 15 minutes walk from the metro station. (with a Blue Star ferry you disembark next to the metro station)

As for the taxi it should be around €20/25 depending on where you are going. The taxi pre-booked or not may be a better option with luggage and a hotel difficult to access by metro

Any accommodations that's near a Metro would work particularly Monistiraki & Syntagma areas.

Staying in Central Athens is your best option to see anything you missed with your first stay.

There's a lot to Athens than just the tourist sites so an extra day may give you an opportunity to see more of what the city has to offer and try more Greek Food which is one of the best parts of going to Greece.

Your best option to get to the airport is to book a transfer which will give you door to door service albeit more expensive than the Metro or Bus.

Rafina is closer to the airport than Athens, and the Hotel Avra offers a free shuttle service to and from the airport.