Starting in Tuscany, ending in Almalfi Coast. Which airports?

Arranging flights is going to depend on where in the US you're starting from. Generally, the smaller the city, the more expensive it is to fly there simply because of supply & demand and economy of scale.

My favorite site for finding airfares is Kayak.com but there are other good ones. One thing to watch out for is discerning whether you're buying directly from the airline, or from an aggregator. The latter is a pain when it comes to making any sort of special arrangements, like ordering an in-flight meal for a family member with allergies. Here is a site that evaluated airfare search engines: https://www.frommers.com/slideshows/848046-the-10-best-and-worst-airfare-search-sites

For more tips about buying & booking, check out the "Tips and Trip Reports" section on this forum under "Transportation"

Will you have 12 days on the ground in Italy, or are you away from home for 12 days (thus only 10 days on the ground)? Giving yourself just 4 days in Rome seems barely enough to get oriented, and it's a fairly long way to the Amalfi Coast (plus it will be mobbed in June). There are coastal places nearer to Rome that you could visit instead, such as Tarquinia to the north or Paestum to the south.

What is your home airport?
Are you planning to rent a car at all? Or are you going to rely on trains and buses?

Flying to FLR and departing from NAP is one option, however those two airports do not have direct flights to North America and you'd need to fly via a European hub (like CDG, AMS, FRA, MUC, FCO, ZRH, etc.).
That works ok if your home airport is a major North American hub with non stop flights to the above mentioned European gateways.
But if your home airport is not such hub with non stop flights to Europe, flying to/from FLR and NAP likely means an extra layover. In that case I'd probably prefer to fly in and out of Rome to avoid too many plane changes.

If you fly in and out of Rome, the best policy, in my opinion, is to take the first train to Florence upon landing (the Rome airport has a train station and you can be in Florence in just over 2 hours).
After visiting Tuscany you should go straight down all the way to the Amalfi Coast (bypassing Rome).
Lastly, you would come back to Rome for the last portion of your stay, from where you fly back home.

Almost no matter where you're flying from in the US, you won't get a nonstop unless it's in & out of Rome, and then only from major US cities. That isn't to say you should do that, but if you're partial to a nonstop--some folks are--that's your choice. Myself, I don't particularly care, as long as the legs are with the same airline (I love Lufthansa), the price is reasonable and the layovers aren't too long. If you can handle one stop, I've found the German airports at Frankfurt and Munich quite efficient, and I'm sure there are others.

If you want to do the 'open-jaw', yes, you would fly into Florence and out of Naples. Make sure you study on this forum about the difficulties of visiting all these locations in high season, and ways to circumvent some of the stress of being in throngs of tourists most of the time. You'll love it no matter what--it being your maiden voyage to Europe--but there are places to visit that might not be as bad as others. I don't handle crowds well as a rule, which is why we travel off-season, and probably why I'm fixated on this aspect of it!

Enjoy your planning!

Just the advice I’m looking for! I’m in NJ so I can fly from PHL, Newark, or JFK. Nonstop is great but one top is fine. We’ll have 12 actual days there, subtracting 2 for travel. I’d love to go at a time of year that was less busy and less hot ( and less expensive!) but I’m a teacher and will be traveling with my 2 school age kids so summer is it if we want to be away for more than a week. We’ll be relying on trains, cabs, and buses, but might be open to renting a car to explore Tuscany where traffic isn’t as crazy. I’m going to check out some of your ideas for alternate locations that will be less busy. :)

We fly out of PHL and use American for direct non stop flights to Rome (FCO) and Venice (VCE). Make sure when you are looking to check if there is a lay over somewhere and the time, remember the times are given in the destination time. My friend got an inexpensive flight to Rome with a layover and change in London at 6 am and didn't realize it was midnight EST, so she not only didn't sleep, but had to switch planes, got through customs in a disoriented state. I'm with Jay about the Almafi coast, we just returned from staying in Sorrento in September and traveling to the Almafi coast via bus. The buses were packed solid and hot and the towns were very crowded at the end of September, can't imagine what they are like in the summer. I think you could consider Rome and the Tuscany area for only 12 days on the ground. You will have plenty to see and do if you keep the vacation between Florence and Rome.

If you can fly nonstop, I would do that in and out of FCO (Roma), and take Roberto's advice to take a fast train from the airport to Firenze. After a day or two there, you can decide to rent a car (or not); there are some good day tours to smaller towns, or you can do them on your own, by train, bus or car. Then train to Salerno, ferry or bus to Amslfi Coast, then finish in Roma.

If you live in NJ, then you can either have a non stop in and out of Rome FCO, or an open jaw to FLR, with one stop only.

Florence (FLR) has 3 to 6 flights a day to each of the following European hubs:
AMS with KLM
CDG with Air France
FCO with Alitalia (although the train is just as fast)
FRA with Lufthansa
MUC with Lufthansa
ZRH with Swiss
Alitalia, AirFrance KLM and Delta are all partners with SkyTeam (so you can code share with any)
Lufthansa, Swiss, United are all partners with the Star alliance.
FLR is connected to other hubs, such as London and Madrid, but not enough daily flights therefore if you miss the compnnection there is risk of rerouting.

Coming back, you might still be better off leaving Rome for last and fly back from Rome.
Naples (NAP) has a lot of low cost airlines flights, but limited traditional airline traffic. Your best option would probably be with Lufthansa, since there are several flights to MUC and also FRA in summer. Other than Lufthansa, choices are limited. Besides you can’t stay in the Amalfi Coast and catch such early flights in the morning. The trip is at least 1.5 hours and you need a car that early in the AM. The best option would be to sleep the last night in Naples itself. But then you might as well go back to Rome, visit for a few days and return from Rome. You save an extra hotel change that way.

If you are really going to the Amalfi Coast (many people think Sorrento is on the AC), then you must reckon with how long it can take to get to any airport. Naples has rather limited service, and bargain air lines can have their downsides. Do you want to fly home in two segments?

Are you reckoning days or nights? This is not a long trip, so it makes a big difference. Since this is your first trip to Europe, you might want to read some our host's free advice, top left.

If you can fly nonstop, I would do that in and out of FCO (Roma), and
take Roberto's advice to take a fast train from the airport to
Firenze. After a day or two there, you can decide to rent a car (or
not); there are some good day tours to smaller towns, or you can do
them on your own, by train, bus or car. Then train to Salerno, ferry
or bus to Amalfi Coast, then finish in Roma.

Yeah, I think Zoe's (and Roberto's) advice here is definitely the path of least resistance. Florence/Salerno is 3 hrs, 43 min on the Frecce train, very efficient and comfortable--we did exactly this run in 2015. And you could easily stay/base in Salerno--a wonderful little city in which we stayed for 5 nights--and daytrip by ferry to Amalfi, Positano on the A.C., Naples, Pompei, Paestum, all an hour or less via train, and get the best of both worlds while really not having to deal with the crowds on the A.C., which I guarantee will not be pleasant. And then 2 hours by train Salerno/Roma Termini. A no-brainer.

Enjoy your planning!

I’m over the moon excited and thought I’d share! Thanks to your great advice we went ahead and booked our flights tonight! We’re going nonstop round trip to Rome and we’ll follow your advice of going straight to Tuscany, then to the Almalfi Coast, then finish in Rome. I’m sure I’ll be hanging around this forum a lot...the vacation planning is just beginning! :))

I'll reinforce the suggestion to stay in Salerno. Besides being conveniently located for day trips to the Amalfi coast towns by bus and ferry, it's simple to get to Pompeii by train, and Salerno has a lovely sandy beach . . . oh yes, and great gelato and pizza.