Flying from LAX to Athens, maybe return from Sophia, Bulgaria?

Why not back up the RS Greece tour with the RS Best of Bulgaria tour?
As a fellow west coast traveler, I'm a little tired of transcontinental + transatlantic flights - so I try to stay on the (European) ground as long as I can.
Several other options pair well with the RS Greece tour...maybe Rome or any of the Italian tours, maybe Sicily or Best of the Adriatic?
My choice would be Bulgaria.
Happy Travels.

Check out Turkish Airlines. If you're not familiar, you may be pleasantly surprised.

By most measures, they're one of the biggest airlines in the world, and they fly to more places than any other airline. They fly nonstop LAX-IST, and should have plenty of connection options from IST to Athens, Sophia and many other places - that corner of Europe is their home base. They're highly rated - surprisingly comfortable seats and generally good service. I think you'll be hard-pressed to do better.

To learn who flies where from an airport, look at that airport's Wikipedia page. Here's the one for LAX: https://en.wikipedia.org/wiki/Los_Angeles_International_Airport#Passenger

David's suggestion of Turkish Air is very good. I only flew them from New York to Istanbul, but they were much nicer than other airlines in coach. As he says, they will have lots of flights through their Istanbul hub to all kinds of places in the region, so you will have one stop service back to LAX.

Turkish Air? Well, an April 10, 2019 direct flight LAX to IST will set you back $1156 in coach economy.

Bulgaria is a fascinating country, but ground transportation links with Greece are challenging at best, so it's not too early to consider how you'd get from Greece to your first Bulgarian stop.

Turkish Air? Well, an April 10, 2019 direct flight LAX to IST will set you back $1156 in coach economy.

Not sure if you think that's an outrageous price - I certainly don't think so.

Actually, I'm seeing $900 round trip LAX-IST for random dates in April, which looks like one heckuva deal to me. I'm sure the price will vary a bit depending on the dates. That's for a non-stop flight (in a coach seat that's more comfortable than you might expect). OTOH I do see flights on other airlines for a few dollars less, but those all involve 1 (sometimes multiple) connections, and probably more sardine-like seats. That would be a very easy choice to me (being blinded by the absolute lowest-possible fare is an all-too-common mistake...it's worth 50 bucks to me to get a good nonstop, avoid 3 connections and miserable seats, but to each their own).

That's just for LAX-IST and back. OP will want to look at LAX-ATH and return from ???-LAX. I'd be surprised if there were better options available than flying Turkish, but OP will need to do the homework. By all accounts I've seen, Turkish is a great airline.

Turkish Air? Well, an April 10, 2019 direct flight LAX to IST will set
you back $1156 in coach economy.

Looking that far into the future is not going to yield any deals (that's almost a year away - airlines probably have some "place holder" fares until the competition revs up as travel dates get nearer). I wouldn't start looking this early because there will be lots of pricing changes until then. Turkish Air indeed has great fares. I've flown them (from the East Coast) several times and liked the price and experience. April is not exactly peak travel time, so I would hold out for a better fare than $1156.

Thank you all, this is most helpful. Turkish Air would never have been on my radar, but we'll definitely give it a try. We paid way more than that to fly to Rome non-stop last month, so the price seems very reasonable.

We considered doing Greece and Bulgaria back to back, but that's too many days away from our plants, hummingbirds, etc. ;-)