Travel from San Francisco to Crete/Naxos

Given that it's a major tourist destination, there are many European airports that offer flights to Crete (Chania or Heraklion) generally from early May to late September, so it's not essential to transit through Athens.

However, some flights are often operated by low-cost airlines (Ryanair, Volotea, EasyJet, Transavia), so it's crucial to check what the fare includes and verify the baggage policy. A flight advertised at an "affordable" price of €50 can easily turn into a €100 flight. Don't forget that everything is extra, even a glass of water.

Aegean and Sky Express, the two (good) Greek airlines, operate flights to/from many cities in Europe. It's up to you to find the best option.

Naxos Airport is a small regional airport with domestic flights to/from Athens only, operated by Aegean or Sky Express using ATR turboprop aircraft.

There are daily ferry connections to the Port of Piraeus (Athens). The ferry journey takes approximately 4 to 5.5 hours, depending on the type of ferry.

Therefore, your flight back to SFO, whether direct or not, will depart from Athens.

You may want to look at skyscanner to get a read on how long these flights will be and best routes. The quickest flight combination I see is on Air Canada from San Francisco to Toronto Person with a 1 hour 15 minute connection. Person to Athens 1 hour 10 minute connection to Athens and a 2 hour and 45 minute connection to Chania. Total time 18 hours.

I am dubious that you will make those tight connections at Person and Athens.

Just my opinion but you might want to re think your plan. After that very long set of connections you will be jet lagged like crazy. Plan to spend your whole trip in Crete. That way you do not have to ferry to Naxos which will take up at least a half day to connect by ferry. Crete is very large so you will have no trouble finding things to do and see.

I just looked at return flights from Athens and they can be done for as little as 16 hours. You will have to get from Naxos to Athens before that return flight.
Can you squeeze a few more days for this trip. Its a shame to spend that much time flying and so little time actually in Greece.

In the high season you might avoid Athens by flying to the islands from other European cities.

Condor Airlines fly from SFO to ATH with a plane change in Frankfurt.

Condor also has an SFO-FRA-CHQ (Chania) flight, that I'm taking in Sept.

I flew Condor to ATH in summer of 2024, and while the flight was fine it turned into a 4-hour delay/missed flight in FRA... But I made it to my hotel by midnight... And then had 20 days to enjoy Greece.

I have to admit we are getting older and need higher end more comfortable business class when doing transatlantic to Europe.
Last summer we took Condor from Vancouver to Frankfurt on business class. Its a great value with excellent service, and I doubt you can get business class less expensive anywhere.

"Naxos Airport is a small regional airport with domestic flights to/from Athens only"

I have to correct you on that @JoLui. In the summerseason Olympic Air has also flights from Thessaloniki (4 times/week) and Crete (Heraklion 3 times/week) to Naxos.

That's right, Nicksy, but in this context I didn't mention it since I don't think taking a flight to Heraklion or Thessaloniki will help in getting back to SFO.

I mentioned it JoLui because the OP wrote "Then should I fly or ferry from Crete to Naxos?"

Ah yes, that's right! And even some HER-Naxos flights for under €60 in June with checked baggage.

That said, it's not the kind of trip I'd take by plane unless I were allergic to ferries.

I'm only allergic to Seajet ferries. I don't like the norms and values of the owner. So, I always avoid using them on
principle.

Marios Iliopoulos and Michael O'Leary could start a company together.... :)