Options from Pisa Airport to Monterosso - Lucca?

There are no direct flights from NAP to PSA. You would need to change planes somewhere. It is much faster to take a train from Naples to Monterosso.

Yes I know - we connect through FCO, but didn't seem like it took all that long. But I will compare with the train times.

As Roberto mentioned, travel by train is the easiest solution on that route. Although the rail schedules for next May/June aren't published yet, they likely won't change much from the current schedules. On that basis, one of the easiest trips will be a departure from Napoli Centrale at 07:31, arriving Monterosso at 14:38 (time 7H:07M, one change at La Spezia Centrale). There are numerous other solutions, many with a change at Roma Termini as well as La Spezia.

When you arrive in Monterosso, I'd suggest a Taxi to the walkway that goes to Hotel Porto Roca. You'll have a short walk as it's right at the end of the "old town", and the rail station is in the "new town". Once you see the pool area, you may wish you had booked more time there! You won't have any problem finding seafood restaurants. You might try Ciak in the old town, Miky in the new town (a bit posh so budget accordingly) or Belvedere in the old town. I'm sure Porto Roca will also have seafood on the menu. Be sure to also try the excellent local Pesto in the area where it was invented.

The flight choice you mention is with Alitalia departing NAP at 11:25 and arriving at PSA at 15:20, after a layover at FCO.

To make that flight you need to be at NAP at about 10:00am, which entails leaving Naples no later than 9:45. Once at PSA, between deplaning, baggage claim, transfer to Pisa Centrale, purchasing tickets, finding platform, you are looking at nearly another hour. I doubt you could catch the 15:56 train departing Pisa Centrale to La Spezia , (which arrives at 17:38), more likely you will have to wait for the 16:56 Frecciabianca and be at Monterosso at 18:17 after a change in La Spezia.

So the entire trip from downtown Naples to Monterosso by plane is well over 8.5 hours. Even in the unlikely event you make the 15:56 train from Pisa C.le, its an 8h journey from downtown Naples.

The train from Napoli Centrale to Monterosso takes from a minimum of 5h38m to a maximum of 7h07m depending on the solution you select. Most solutions take around 6 hours and require two changes (Roma and La Spezia). The one suggested by Ken requires one change only, but it's a slower Intercity train (plus you need to get up early).

There is one solution departing from Napoli Centrale at 10:05 (near the time you'd need to be at the NAP airport), that will put you in Monterosso at 16:05 after a change in Rome and one in La Spezia. With the flight option at 16:05 you'd still be in Pisa waiting for the train.

The only way you could make it faster by plane is by flying non stop from NAP to GOA (Genoa), then taking the train from Genoa to Monterosso. In that case you might save maybe an hour over the all train option. I think Volotea flies non stop from NAP to GOA. Not sure about Alitalia, but you can check.

To address another part of your question, I think spending 2 nights - 1 full day in Lucca would be a nice change of pace from Amalfi Coast and Cinque Terre experiences. I'm not a big fan of 1 night stops, but you might be able to make that work by departing Naples between 9:00 and 10:00 so that you arrive in Lucca early-to-mid afternoon, and then continue on to Monterosso the following afternoon.

Since everyone is so set on us training it, why not depart from Amalfi & save the private car transfer to Naples? And thanks for the Lucca support & Monterosso info!

Nobody is set on anything. We give you the options, then you choose.
You can also fly from Naples to Pisa via London or Munich if you prefer it to the train. It's not what I would do, but since many Americans are more familiar with flying than on trains, you can do that too.

There are no trains on the Amalfi Coast and transportation from there is a bit convoluted.

The closest main Trenitalia train station is Salerno, which can be reached by boat or bus (or also by car). That is probably what I would do. If you can make it to Salerno before 10am, you can make it to Monterosso still at 16:05.

You could also take the bus to Sorrento, then the Circumvesuviana commuter train to Naples.

I've lived in Europe twice and Eurailed all over for 6 months twice too, so am keenly aware of how superior the train system is. My husband has back issues & a short flight, even though a hassle to get to the airport, etc., might be best. Or... being able to get up and walk around on a train might be best. Just looking at all options and I think you've convinced me to give the trains NAP/CT a try. We are from Monterosso to Nice. Thanks for the Salerno idea. And still pondering Lucca. Just wish it were end of May already. Got back this June & started planning the next trip again immediately to have something to look forward to!!!

I think it would be easier for your husband's back to take the train, much more opportunity to walk around, no seatbelt constraints.