Where should I have my flight layover on the way from San Francisco to Greece?

What are the options? I think this works better if you do a search and then ask us about the choices, though possibly someone will do the legwork for you or just know off the top of their head.
Turkish Airlines is great, especially if you are going to stop over in Istanbul.

Are you just asking about what connection city to choose for your flights (a simple and generally non-critical choice), or are you planning to stop somewhere, sleep, and spend time there on your way to Greece (a much more complex choice)?

Consider this: Do you actually have "time to kill" on your way to Greece (that is, your Greece itinerary has plenty of days to easily get everything done that you would like to)? Most folks asking questions here about trips to Greece turn out to have greatly underestimated the time (number of days) they would need to check off all their Greece hopes and dreams, discovering too late that getting around a lot of Greece eats hours and days at a shocking rate (I confess to having fallen into this trap myself).

I only mention that because it is so common for people to begin planning a short trip (that's two weeks or less) with a long list of mainland and island "must see" places, and they're often disappointed (and in denial) when they work out the time that's actually needed for for the trip they want (which means they have to cut half of their hoped-for destinations). So, before you contemplate spending a leisurely couple of days at some stopover city (which is a nice luxury if you can make it work), just consider how that would impact the time you have to spend in Greece itself and your list of destinations.

For most folks, unless you really do have plenty of time to kill, it's usually most efficient to just get there as quickly as you can, without making extra stops along the way to sleep, tour a bit, and eat up a few days.

All that said, there are no nonstop flights from the US west coast to Athens (or anywhere else in Greece). So you have to connect at least once somewhere. My preference is always to get the long trans-oceanic flight outta the way first, connect someplace (once) in Europe, and continue on to your actual destination before you stop to sleep, and do that as quickly and efficiently as you can. Others have different preferences.

On the way home, that's another question entirely. For that, I love Istanbul. Turkey (beyond Istanbul) is indeed awesome and is absolutely worth a dedicated trip of its own when you can manage that. Istanbul also makes an ideal place to stop and spend a few days at the end of a trip to anywhere nearby - but again, keep in mind any day you stop somewhere else (like Istanbul) is one day less you have for Greece. Turkish Airlines (which is great, too) has nonstops between Instanbul and SFO so it's an obvious option to consider. Their prices are good and you will be pleasantly surprised at the experience of flying with them (I go out of my way to fly them and do so often).

I would look for a city with a direct route from SFO then direct to Athens depending on what interests you. I remember a long haul the time we went from SFO to Athens, a break in between would have made the trip more enjoyable.