So we are considering returning our rental car around 4am at the airport before we fly out at 6am. Is this possible? It would solve a lot of problems of where to sleep that night. We are traveling with 5 adults.
You will need to contact the local office for the rental agency where you propose to drop off the car. People here can only give you general suggestions.
IME most larger rental agencies have things set up to do this (those at airports usually do). Often smaller offices may be set up for this, too. Exactly how you do it varies - there are typically instructions posted at the drop-off point, though they may not always be crystal clear.
There is one potential gotcha. You drop you car there at oh-dark-thirty, when nobody is around. You drop the keys in some slot, head off to your flight and forget about it. A month (or a few months) later your credit card gets hit with a charge for "damages" to your rental car...
Do you have proof there was no damage (or that scratch was already on the car when you picked it up)? If not, you're not in a very strong position to defend yourself. If there's a human staffing the place when you drop off your car, you can (sometimes) get them to acknowledge the car was returned in good condition (and with a full tank of gas...). With nobody there to validate your claim, it can become more squishy.
You can protect yourself somewhat by being very careful to fully document the car's condition both before and after the rental, keep a receipt for the gas tank fill-up with a clear time-stamp on it close to your drop-of time, etc. But it still feels like a system that relies to a great degree on "the honor system" (and there are some car rental offices that don't have an excess of "honor").
Personally, I've never had trouble with dropping off a car at an unattended office, but I've read stories from others who have run into alleged shenanigans and were left with a bill for that. If you do this, just take all the steps you can to cover yourself in the event you get some "surprise" after the fact.
We will most likely be renting a car from Hertz at the Athens airport. I know in the states we've dropped it off that early and there are people working at that time, just wasn't sure about Greece.
I figured it out. I found a great Airbnb within 10 minutes of the airport that had 100's great reviews. The owner provides transportation to and from the airport at any time of day. So we can dropped off our rental the day before we leave and get a ride to the airport for half the price of a taxi at 4am. The price of Airbnb is the most affordable for a group of 5 adults especially around the airport. Thank you for the warning about dropping your rental off in the middle of the night. I feel much better about this now.
The big companies have a pop up box for each of their authorized agencies, which lists their hours. Drill down to the highlighted return station in their list, and click on it to learn the official hours.
Although I haven't rented a car in Greece, I will add that another issue is finding a gas station open at the time of your return, one which will accept your credit card (Americanski Chip and Pin? Chip and Signature? ... ... ) if it is open but UNATTENDED at that hour.
Really depends on your company. We did exactly that in Santorini and the company was fine with us just leaving the car parked and putting the keys in a box. In Athens, we met an actual person in the dropoff area so could not likely have done that at 4 am.