Flying

What’s more convenient for you?

Use Google flights to check your options
Set up flight alerts
Book with the actual airline-never a third party reseller

I’d want the longest leg to be from home to Europe -that will give you the most time to sleep-leaving later evening if possible so it’s close to your usual bedtime

Change in Europe will be in the am and usually just a short flight onward to Rome

Where do you change planes? Is this for your flight to meet up with your cruise?

I'd probably do it all in one whack. I fly from the Inland Northwest so have at least 1 stop to get anywhere and 2 stops to get to Italy. I just want to get it done.

Coming back home, depending on where in Italy you end up (or it looks like you said your cruise ends in Athens?), I might break it up by staying in Amsterdam on the way back. Few direct flights from Italy to connect to something in the Northwest without leaving really early in the AM so I would fly to Amsterdam at a reasonable time the afternoon before and then catch my flight to Seattle the next morning.

I prefer to fly from the US in the late afternoon or early evening. Sleep on the plane. Arrive in Rome in the morning.

I'm guessing you have to connect to a hub outside of Ohio to get a direct flight to Rome. So, you also have a choice on flying west to say Chicago or east to say New York for your connection. The hub-to-Rome time will be a choice you can make. I live in Arkansas and prefer DFW over Charlotte as the flight is a little longer and gives a little more time to sleep.

IMO avoid connecting to Rome through any UK or Eurozone cities if you can. In other words, make your connection before you sleep. Flying home is less important where you connect as you should only nap, not sleep as you travel west.

I live in Ohio and have flown to Rome a few times. I usually fly to New York (about an hour from my home airport of CLE) in the afternoon, then fly overnight directly to Rome. From NY there are earlier evening and later evening departures, I actually prefer the earlier evening as it takes time to takeoff, get through meal service then settle in for the night. Plus, if the flight is canceled may be options to get on a later departure.

I expect that all three of the major US international airlines, Delta, American and United have direct flights from the USA to Rome.

I know Delta has one from Atlanta.
American has hubs in Charlotte, NC and Philly, PA. United has a hub in Chicago and another in Houston (I think or perhaps it is DFW).
All likely have direct flights from NY at JFK. However, I can don't like going through Chicago and JFK, I have had delays there in the past.

Check out Kayak.com for flights and it will give you the cheaper flights, but perhaps flights from all airlines.
Delta has a search function that allows you to search for flights with only one stopover. They have flights out of Detroit as well.