Fly in to Rome or Florence

Where does Venice fit into your question??

It doesn’t. Subject should be Fly into Rome or Florence. I edited. Thanks! 🤦‍♀️

There will probably be a different routing to fly to florence- usually connects via Germany or Switzerland. So you will have to connect after landing in Europe. Maybe with Rome too, but its possible to go direct from USA to Rome.
If you are concerned about jet lag I would fly into the place you are staying that night. Though getting a taxi from the Rome airport to the Termini is not hard - you can arrange in advance. And buying tix in the train station is really not difficult.

There was a direct train from Rome airport to Florence a few times a day that we took…

I would definitely look at the routing and number of connection for Florence vs. Rome. I personally prefer fewer connections and make that a priority.

That said, you don’t have to leave the FCO airport to get the train to Florence. It’s literally a five - ten minute walk once you clear customs and immigration. There are bright yellow signs, so it’s all pretty straightforward. We’ve done it twice now and I used Roberto da Firenze’s step by step instructions that he gave on this forum. But there really are signs everywhere to point you in the right direction.

I would agree with flying into and out of Rome because there are probably better flight options. It is easy to take the train to Termini and as you know from your previous visit, you don’t need to speak Italian.
It would make more sense, however, if you visited Florence after your cruise.

getting a taxi from the Rome airport to the Termini is not hard

Expect to wait in a long line and my first time in Rome there was a strike so the line didn't move. Strikes are not uncommon in Europe when relying on public transportation.

There was a direct train from Rome airport to Florence a few times a day

From what I can see there is one direct train from Rome’s Fiumicino Airport (FCO) to Florence’s SM Novella station departing at 1:53p: https://www.trenitalia.com/en.html. Maybe there’s more during the summer.
Most likely you’ll encounter an additional air connection if flying into (or out of) Florence. However, if you fly into Rome chances are you’ll arrive in the morning and will have to take a train to Rome’s Termini station to get to Florence’s SM Novella station. I hope you pack light since you’ll spend more time hauling luggage meaning more bruises if a train connection is involved.

We have flown into FCO 3 times in the past few years and never waited more than a few minutes in the taxi line if at all
It’s very organized

If your home airport is SDF the issue with flying to FLR is that you will need to have two layovers, one in a US hub (like Atlanta or Newark), then another one in a European hub that has flights to Florence (like Paris CDG, Frankfurt, Munich, Amsterdam, Zurich, Rome, Lisbon, Madrid). Whereas if you fly to Rome, you will need only one layover (likely Atlanta or Newark). Taking the train from FCO to Florence is not a big deal. There is a train every 30 min from the airport to Roma Termini and trains from Termini to Florence are every 15-30 min. The only issue I like to emphasize when traveling by train is that you need to be judicious with your packing because you are responsible for carrying your suitcases on board of the trains (two steps up) and placing them on the overhead compartment or the storage hold near the train car entrances. So pack light and preferably in one carry on size suitcase only.

In your case I wouldn’t bother with a taxi from the airport to Termini. The Leonardo Express train will place you already inside the Termini station although in a different platform compared to,the one where the Florence bound trains depart, the Leonardo express is also faster than a taxi and for two people it is €20 cheaper (€15 per person rather than €50 for a taxi ride).

You can buy the train ticket all the way to Florence at the FCO station.

We have done both. Once flying into Florence, we were redirected to Bologna and then bussed to Florence - not fun. Taking the train from FCO is easy and to me a great chance to nap a couple hours before hitting the ground running in Florence.

I would suggest fly into Florence for your stay, train to Rome for your stay, do your cruise out of Rome and fly out of Rome.

Flying into Rome requires extra train ride to Florence (additional cost and time). If you train to Florence directly after arrival at FCO, you will suffer a really long travel day including the plane ride. If you stay in Rome first and then travel to Florence before you depart on Cruise from Rome, you either split your Rome stay and have an extra hotel check-in/out in Rome or stress out travelling directly from Florence to embark on the cruise ship. I would only consider flying into Rome if the flight to Florence required significantly higher cost or an extra or nasty long stopover.

We did something similar in 2015 but flew into Venice and out from Rome (Venice-Florence-Rome-Med cruise). The cruise ship returned to Civitavecchia (Rome) by 7AM. We transferred directly to airport from the ship and flew out that afternoon without need to stay another night in Rome.

It really comes down to the number of flights, how they are routed and price, doesn't it?

Florence isn't a "real" airport in the busy international sense, so you'll be changing somewhere in Europe first.

Rome is easy.