Get Around Southern Italy without a Car

Sorrento is a slower pace than Naples, which is a large vibrant, albeit chaotic, city. I think you will enjoy staying in Sorrento more.
There is a bus that takes you directly from the NAP airport to Sorrento (Google curreriviaggi). It costs only 10 euro pp, (a taxi to Sorrento is more costly, about 80 euro).
From Sorrento it's very easy to visit Pompeii (Circumvesuviana train), Capri (boat), Amalfi coast including Positano and Amalfi (bus) and even Naples (Circumvesuviana train).
Roads are very narrow on the Amalfi coast, therefore I don't recommend renting a car unless you have very experienced drivers. Leave that job to the bus drivers.
Note that some of those villages on the Amalfi coast and also Capri, are perched on the cliffs therefore steep uphill walking (sometimes on steps) may be required in those villages.

We agree with Roberto's advice to stay in Sorrento for both a pleasant town and ease of day-trip transportation. Rick's Italy book has pages of detail about local transport and hotels, but not apartments. http://www.sorrentotourism.com/en/accommodation.php could give you some more ideas.

We flew into Naples in 2012 and took the bus from the Naples airport to Sorrento (with our luggage stored under the bus). We loved Sorrento! It was slow-paced and wonderful to stroll around at all hours. It had reasonable restaurants (the best pizza!) and a grocery store. We day-tripped from there using public transportation to Pompeii, Herculaneum, Paestum, and Naples. (We chose not to go down the Amalfi Coast or to Capri, but those are options.) We stayed 4 nights at Ulisse Deluxe Hostel (in a private, ensuite, air-conditioned room with breakfast) and loved it, but it was a ways from the Sorrento Circumvesuviana station if walking is an issue. We had a fabulous time. Hope you have a great trip!

Sorrento sounds like a good base. Paestum is a little further south along the coast, but you can get there by bus. If you had more time in Italy, Another place of interest in the south is Matera (read a little history of the town first). If you are interested in the trulli houses of Puglia, you can get to Alberobello by bus from Bari. All these places provide different types of sights and experiences.

Do not take the Circumvesuviana train from Napoli, take the bus.

Thank you, everyone. Valuable advice.

We are considering a similar trip next spring with two young granddaughters, also flying into Naples. We're looking for a quiet, smaller place to recover from jet lag and be convenient to Pompeii. So we are considering the small town of Vico Equense (between Naples & Sorrento) -- specifically the Cubo Apartments (http://www.cuboapartments.it/it.html) for our first 3 nights. They get great reviews on Trip Advisor and Booking.com. You can reserve now on Booking.com without paying anything and cancel up to a couple of days before you arrive with no penalty. Compared to Sorrento, Vico Equense would be closer to Naples, and a shorter trip to Pompeii. It's smaller than Sorrento, and appears easier to walk around. The hotel is near a train station, gelato, restaurants. We've never been here, but it might be something for you to check into.

No matter where you stay, I would suggest contacting your hotel and ask if they could arrange a transfer for you from the Naples airport to the hotel. That way, someone would be waiting, with a sign with your name on it, when you get through baggage claim. When you're tired and jet-lagged, it's wonderful to have someone pick you up and drop you right at your hotel.

I agree with the suggestion not to drive down the Amalfi coast unless with a very experienced driver. However i would highly recommend the trip by boat from Sorrento down the Amalfi coast and back. Check timetable of the various boats.
We frequently use airbnb and also booking.com for accommodation.

People make a monster out of a minion regarding driving down the Amalfi coast route. Just be patient, and have a driver who is okay with driving instead of sightseeing - if there is a couple, on the way back they can switch places so that other person takes the wheel allowing everyone to take views without dealing with the chaos of buses.

This being said, Sorrento works fine as a home base, it has trains that connect it easily with the archaeological park in Pompeii and central areas of Napoli. Vico Equense is fine, it also has a train station, though it doesn't have the variety and choice of fine dining offered by Sorrento. Boats to Capri leave from Sorrento. There are frequent trains connecting Napoli, Pompeii, Vico Equense and Sorrento (and other stations as well).

Paestum has an adjacent train station as well, but is located in other line. To travel between Sorrento and Paestum by train you need to transfer either at Napoli Central (with some backtracking) or from Torre Anunziata to Torre Anunziata Città (half a mile on foot between both stations).

My husband and I are booked for four nights at Cubo Apartments in Vico Equense. Sept 16/2014. Is this area ok for getting around without a car? We hope to take a couple day trips. Does anyone have suggestions on best use of our time while in that area? We have never been to italy and wanted four days on Amalfi coast before joining our tour which will depart from Rome.

Linda, it's really late to ask that question, especially piling-on to another thread.

However, if this Google Maps accurately describes your rental, https://goo.gl/maps/wSiGQ , you're going to be fine. It's very near the Circumvesuviana commuter-rail service. Since I never got off at Vico Eq., I don't know if stairs or an elevator are involved - there is an elevator at the Sorrento Circumvesuviana station, although the platform can be very crowded when the arriving train is full.

As a matter of accuracy, you are not staying on the Amalfi Coast, and you wouldn't be if your rooms were in Sorrento. But don't feel bad about that: You can't see Vesuvius from the Amalfi Coast, and you can from Sorrento and V.E. You are perfectly located for daytrips, although you need to research your Amalfi Coast trip. Most people (... who don't stay on the A.C., that is) stay in Sorrento, which is the origination point for the vastly overcrowded bus to Positano. At worst, you'll take the train to Sorrento, walk down the ramp to the bus stop, and get in line with everybody else. I think you'll have to take a local bus in Sorrento if you want to get a ferry.

Maybe you've saved enough by staying in a smaller town than Sorrento to hire a car and driver to visit the Amalfi Coast, as we did from Sorrento. But it does get expensive. Your location is perfect for Pompeii or Herculaneum.

Andre, how did you find parking, so that you could walk around Positano or Ravello?

@Tim There are at least 4 parking lots tucked into the mountain with guys running out to tell you they have room. Ravello has a lot on the before you hit the main piazza.