8 hour stop over in Athens

Its possible. You don't say where your flight originates, but plan on at least an hour to get through customs and immigration and rechecking your bag. Then another hour to get to Syntagma by Metro. On the way back its another hour to get the airport, and then the time to get through security (less than an hour, assuming you checked your bag before you left the airport, and already have your boarding pass). So overall 4 hours in travel and processing time, leaving you four hours in Central Athens.

With four hours, you could walk the Acropolis, do the National Archaeological Museum or Acropolis Museum. What I personally would do is just walk from Syntagma, down through the Plaka, and back up to get the Metro at Monastiraki, shopping and eating and enjoying the city.

So the question only you can answer is: is that worth the 4 hour rigmarole to get there and back?

If all you are able to see are the Acropolis and the Acropolis Museum, my opinion is that it would be well worth the effort. For us, seeing the Acropolis in person after having seen it in pictures and movies for so many years, was a great experience.

Just as importantly, the Acropolis Museum is arguably the finest archaeological museum in the world; being able to see the excavations beneath your feet as you walk through, then seeing the amazing exhibits, provides a profound experience.

Depending on the time you arrive at the Acropolis, you may encounter a crowd, but you can probably get a ticket ahead of time--I was there with a group so didn't have to buy tickets myself--I'd strongly recommend that. You can walk through the Acropolis in an hour, spend another hour, perhaps two, at the museum, and be on your way again.

If you have even more time left, you could stroll through the Plaza district (the old town of Athens), which is really nice; if you see the meat and fish market, its worth a quick walk through--like nothing I've seen anywhere else.

Since your time is limited I think a private driver is the way to go. We used My Athens Transfers for a day in Athens recently. They are not licensed guides and won’t walk you through a sight but will provide lots of info and get you where you need to go quickly and efficiently, saving time. I would also prioritize the Acropolis and the Acropolis Museum. Familiarize yourself with these sights by reading Rick’s guide book and perhaps copying his maps and you will be fine on your own. With any leftover time your driver could show you some of the other sights like the temple of Olympian Zeus (although currently under much scaffolding), the Panathenaic stadium and Syntagma Square with the guards in traditional uniforms or just have him take you to the Plaka for lunch. I would pre-purchase tickets for the Acropolis and the Museum but you won’t need tickets for the other sights. Might be a splurge but much better then sitting in the airport for eight hours.

You do not have 8 hours to visit central Athens. By the time you have deplaned, claimed baggage, done the transfer, got into Athens, you could have used up 3 of your hours. Then you need to get back to the airport two hours before your flight to Crete, so up to another three hours. Also, you would be in central Athens in the heat of the day … and it is 35C (over 100F) today! Maybe think about heading to one of the beach towns that are quite near the airport, Artimeda, Vravrona or even Rafina. Just relax, have lunch at a beachside restaurant and then head back to the airport. When I have had similar length layovers at Athens, I have just stayed at the Airport. There are some interesting exhibits on the second floor of the departures level of artifacts found when building the airport.

You should have specified what time is your flight to Crete. This would make advice more effective about the real time available to see Athens.

The arrival in Athens is from where? What the origin of that flight is determines whether you need to go through passport control/immigration which will eat into your available time.

Will you have checked bags and can you drop them off that early? What will you do with your carry on ? Assuming there is storage, you still have to factor time to deposit and retrieve them

If your flight out is at 5PM, you really do not have time to do more than get into Athens and have lunch at a restaurant that has a view of the Acropolis and meander for a bit and head back to the airport.

Factoring less than an hour each way for travel to/from the airport is unduly optimistic.

And if your incoming flight is late......

I’ll be flying in from Boston in the US. We arrive in Athens at 9am and leave at 5pm. So we would need to venture out at like 11-noon which is also the middle of the night for us. And I can imagine Athens will be pretty busy. Would anyone recommend a closer destination or restaurant we could go to and relax that isn’t far from the airport?

When you will leave the airport and its air-conditioned halls it will be around 10am / 10.30am. The first seconds outside will make you understand why Lesley advises you to go to a more airy place near the sea rather than staying 2 or 3 hours in the unbearable heat and pollution of Athens.

Artemide or Rafina are 20/25 minutes from the airport by taxi.
To avoid walking around town looking for a restaurant the port of Rafina would be a good option. All the restaurants in the port are lined up on the quays and the taxi rank is right next to it. (and you will get an overview of some ferry departures/arrivals).

Plan to be back at the airport at least 1 hour before your flight if you have no luggage to check in and your boarding passes ready - 1h30 would be safer in July

Can we check luggage to Chania 6+ hours early or do we need to keep it with us?

I assume you are taking the 5:15 p.m. Sky Express flight to Chania. (there is no flight at 5 p.m.).
Download the Sky Express application you will get your boarding passes 48 hours before the flight.
You can also print them at home before leaving.

Note that if it is a sky express flight, there are baggage weight limitations depending on the fare chosen.
You must have booked the "Sky Enjoy" rate for a piece of luggage up to 23kg. The "Sky Joy+" fare only entitles you to a maximum of 15kg.

If in doubt see here:

https://www.skyexpress.gr/en/sky-experience/before-fly/fare-types

3 or 4 hours before the flight is not a problem for dropping off luggage. 6 hours with Sky Express, I'm not sure.

Anyway you will have to check on the departures level which is on the floor above the arrivals level.
Go there as soon as you have collected your luggage, there may be a lot of people at the departure check-in counters

If it's too early you can leave your luggage at "Care4bag" located inside the arrival hall next to Gate 1.
For 6 hours it's €8 to €10 per bag depending on its size.