Flights

That's plenty of time if nothing goes wrong, but what happens if your flight back to Athens is cancelled or there's a long delay due to mechanical problems? It's always best to return to Athens the day before flying home.

You didn't say what airline you are flying back on-I know that Aegean is part of either the DL or UA alliance-can't say which, however, when you book, there is a drop down window asking who you might be a member of. If continuing with the partner, bags would be checked through and if any problem, you could be taken care of under EU rules.

I agree that it would be much better to get to Athens one day before you fly. Flying out of Athens the same day after coming from an island can be risky: delays, cancellations, bad weather, etc.

Play it say and spend the day in Athens then take the flight the next day. It will be less stressful, plus you get a day in Athens which will give you a tease of how nice a city it is, even if many don't think so.

Aegean is an excellent airline and has won awards for the past several years. They are reliable but mechanical problems and weather can still happen. We have witnessed several people scramble to change their bookings when we experienced a 4 hour delay on Naxos a couple of years ago. Its probably about 99 percent probability that your flight plan and connection will work. Is it worth it to spend that last night in Athens. Yes it is but that is your call.
By the way Aegean is a star alliance member so that means United is the American airline you will be looking for to book connections with Aegean.