I'm still a bit confused about the OP's plan.

BUT, the OP could get right off the plane and take a trenitalia train to Salerno. Then walk 200 feet and board a ferry to Amalfi that takes perhaps 30 minutes. Amalfi is a neat town but really not that much to see.

Spend one night in Amalfi and then take the ferry and then train to "New Pompeii." Store your luggage at the station or the entrance to the ruin. After touring Pompeii take a fast train to Rome.

I personally think three nights in Rome is plenty unless there is a list of things you want to see and do. Since you are arriving late this will give you two full touring days.

This leaves the OP with five days. All of these can be spent in Florence and the OP can take side trips to Pisa and Sienna. One CAN do a day trip to Venice, and I think it's better than nothing. But the OP can also spend three nights in Florence and then leave early for Venice on Day 8 and spend the last two nights in Venice before flying out of VCE.

Everyone seems to want to spend time and spend time and spend time in Rome. For me personally, once I've seen the Coliseum, the Vatican, and a few other sites I'm ready to go elsewhere.

>>>BUT, the OP could get right off the plane and take a trenitalia train to Salerno. Then walk 200 feet and board a ferry to Amalfi that takes perhaps 30 minutes.<<<

Maybe, but the OP said she wouldn't arrive until noon. It would depend on how long it takes to clear the airport (retrieve luggage) and get to the train station in Naples (there is no train station at Naples airport) and whether a ferry is available at that time. Ferries don't run anywhere near as often as the Sita buses and you may have a two hour wait for a ferry. The train station in Salerno is not within 200 feet of the ferry.

>>>>Spend one night in Amalfi and then take the ferry and then train to "New Pompeii." Store your luggage at the station or the entrance to the ruin. After touring Pompeii take a fast train to Rome. <<<

Not practical and some of it not possible. If you take a ferry from Amalfi to Salerno, you have a trek with luggage to reach the train station from the port. There is a gap in Trenitalia train service in the mornings to "new" Pompei and there is no luggage storage at the Pompei train stations. The Pompei station on this line is not close to the entrance of the ruins (it's about a mile away). The closest entrance doesn't have luggage storage either. You would have to get transport to the other Pompeii entrance farther away (by the Circumvesuviana train station Pompeii Scavi) if you wanted to store luggage. There is no fast train from either Pompei station to Rome. That would be a very tiring first two days after overnight flights.

If Pompeii is a priority then you should leave it in your itinerary, but you really need to add some time to the area if you plan to visit the Amalfi coast also.

It would be simpler to take the Alibus from the Naples airport to the port and catch a ferry to Amalfi (check ferry schedules!). That way you could see the entire coast area as you would pass Sorrento and Positano on the way .

Kybourbon is right about the distance from the train station to the ferry. It's more like 900 feet based on Google maps. I remember it being closer. In any event, it is a very short walk.

Certainly the better way of seeing Pompeii is with the Circumvesuniana commuter train between Sorrento and Naples. But one can use the train stop for the new city and I would presume take a cab and thus make use of luggage storage.

I could make it work for me, but it obviously requires some research into train and ferry schedules. Of course it might be easier to start in Rome and take a day trip to Pompeii. Not a quick trip, but perhaps easier than trying to work in a one-night stay just to see Pompeii.