Originally Posted by UKtravelbear

OP posited an option with a 5 hours layover as well.

But the OP does not have 10 hours at all. (or 5 if they chose the shorter layover)

OP need to allow time to clear Greek immigration for starters. I've no idea how efficient (or not) it is at the arrival time of the flight from Cairo. US citizen will likely be in the non EU passport line which can take longer.Then find the locker for your bag - check ATH website for left luggage facilities.

Then you will need to be back at ATH however long before your departing flight your airline requires you by to clear security for your flight to Israel.

Further subtract the time taken to get to/from wherever you want to be in Athens city. On the return you'll want to allow extra time to allow for transport delays

OP has a lot less time than they think they have.