Greece then Italy

Delphi is a 5 hr rt drive. It can be done as a day trip, but spending overnight would be nice.

Athens is the closest airport to Delphi

Logistics are important so lets see if we can tweak you plan a bit to make it more efficient.
Normally I would suggest you do take that flight to santoirni on day of arrival however with your plan I would say do your time in Athens att eh beginning of the trip. Once you are over jet lag rent a car and drive to Delphi. Time it so you arrive mid afternoon check into your hotel then visit the museum wander the village marvel at the views down to the Gulf of corinth. Next morning get to the site early and you will have it pretty much to yourselves for abut 2 hours until the Tour buses from Athens arrive. By then you are at the top top and it will be another hour before the crowds reach you. Its an ideal way to see Delphi. Now return to Athens or better yet head north to visit Meteora. It is an outstanding site. Use the sme strategy. Arrive early evening and drive up to the Monasteries. There will be a few people around but for the most part it is deserted. Get your photos. Enjoy your evening in Kastraki the little village nestled at the foot of the mountains. Next morning get out early and hit your chosen Monasteries10 Oclock the site will be full of tour susses. You can tough it out or drive back to Athens then. It is a 5 hour drive however the combination of Delphi and Meteora is unbelievable.
Finish Athens. Fly to Santoirni. When you are finished in Santoirni fly direct to Rome. I did a dummy booking on Aug 18 and there are at least 4 direct flights to Rome.
Olympia Delphi Meteora https://www.flickr.com/photos/stanbr54/sets/72157645469717811/

Thank you so very much!! The idea of flying from Santorini to Rome has really helped!!
And I like the idea of spending a night in Delphi too. There is so much to do!
Again, thank you.