Traveling from Florence to Athens

In your case I would go to Florence immediately by train upon landing. Just a couple of hours from Rome Fiumicino airport.
After Florence I’d go to the Cinque Terre by train.
Lastly from the Cinque Terre I’d go back to Rome via train, through the coastal route.
In other words you’d leave your Rome visit as the last portion of your loop.
From Rome there are plenty of flights to Athens (with Agean, Alitalia, and RyanAir from CIA airport).

Another alternative would be to fly to Florence, instead of Rome. Then do the following itinerary:
Florence > Cinque Terre > Rome > Athens.

Unfortunately there are no flights from Florence to Athens.

Aegean Airlines is starting a seasonal flight from Pisa and from Bologna in June, but I doubt it will be every day of the week, therefore it may not work for your schedule. RyanAir, a low cost airline, currently has a flight from Bologna to Athens.

These are the options, see what works best for your dates. Go to the aforementioned airlines’ Websites.
Airport codes:
Rome: FCO and CIA
Florence: FLR
Pisa: PSA
Bologna: BLQ
Athens: ATH

Pisa Airport is about half way between the Cinque Terre and Florence (about 90 min from either). BLQ is less than 90 min from Florence.

Thank you so much Roberto!
This is very helpful information as I feel like I don't have any idea what I am doing as far as the routes of travel yet:)
May I ask you also if you would recommend any villages of Cinque Terra over other parts?

Thanks again
Abby

Personally I think that Italy and Greece should be two separate trips, not part of the same trip, especially because I don’t have a feel that your trip is a long one. Italy deserves at least 2-3 weeks. Greece at least 8-.10days. But this is your trip not mine.

Of the 5 Cinque Terre villages (Cinque means 5 in Italian) I prefer to stay in Monterosso, the largest of the 5. Vernazza is the most popular and famous, but also the most crowded. Manarola a nd Riomaggiore are nice too. I find Corniglia inconvenient because it’s on top of the hill and the train station (and the sea) too far down to walk (although there is a shuttle bus).

abby,

Another route you could consider is Rome > Florence > Cinque Terre > Milan > Athens. If you stay in Monterosso, the longest travel segment by train will be Monterosso to Malpensa. Depending on which train you choose, travel time will be about 4H:22M, with a minimum of one change. You'll travel first to Milan Centrale and then to either Malpensa T1 or T2, depending on which airline you choose.

Aegean Air still has daily flights (AFAIK) and I've flown that route in the opposite direction. Aegean is a "class act" in my experience, and I'd certainly recommend them. You could also use EasyJet from MXP T2 and I also recommend them. However they only offer daily flights during July and August. At other times there are no flights on Tuesdays and Thursdays. If you decide to use EasyJet, be sure to read their "Terms & Conditions" carefully, especially related to luggage rules. I've found that the flight is a lot nicer if one chooses Speedy Boarding and Advance Seat Selection (at extra cost of course).

Thank you so much for your kind responses. They are really helpful. I think I may consider making this mostly a Greek trip vs. a italy/ Greek trip. It sounds like they might be a wiser idea seeing that we only have 12 days in Europe:) if anyone has ideas on their favorite islands to visit in Greece, that would be much appreciated:)

Abby

Just to clarify: You're flying into Rome and out of Athens?

You don't have a lot of time, and I would agree that since you must go to Athens anyway, it's best to make the trip as much about Greece as possible. (Honestly, I'd probably forget Italy on this trip.)

Ideally, you'll fly from Italy to an island on the day you switch countries. If you can do that on a single ticket (even with a possible change of planes in Athens), it will save you time, because you won't need to build in a big buffer to protect against a delay on the Italy-Athens flight. If you must buy two separate tickets on budget airlines and the first flight is late, you'll be on your own to buy last-minute replacement tickets to get to your island destination.

On a short trip, it's especially desirable to put all your Athens time at the end of the trip. That cuts out one hotel change and some travel to and from the Athens airport. It will make your time in Greece more relaxing, because you won't need to worry about making it back there for your flight home. Ferries and flights to and from the islands do get canceled on occasion.

Yes we are flying into Rome and out of Athens. Since we already have our tickets booked to Rome, I think we will tour the Vatican and sites there for 2 days and then follow your advice and fly straight to one of the Greek islands and spend the remaining 9-10 days in Greece. Does that sound like a good plan? I think we would like to visit Santorini and Naxos unless anyone has better ideas. Open to any suggestions!:)
Abby