Positano to Naples

It would be a very long day, but you could take a bus or ferry to Salerno or Sorrento, then change to train.
What time of year will it be?
I'd consider building in a stay in Naples to see it and Pompeii, then move to Positano.

We would be there in mid September

Positano is not a good base for doing day trips to Pompeii or Naples.

If you do not want to stay in Naples, then I think the best alternative is to stay in Sorrento and do your day trips to Naples and Pompeii from there. Make Positano a separate stop.

I agree with Joe32F. Unless you have a specific reason to stay in Positano, I'd recommend Sorrento. It's very easy to get from Sorrento to Naples, Pompei, or Herculaneum on the train; it's easy to get from Sorrento to Positano on the ferry or bus. And Sorrento is way more interesting than Positano, with much more to do and see. And it's cheaper!

Agree with Joe-stay in Sorrento-great city for shopping, restaurants & views...
easy ferry ride to Capri & Naples and cheap bus ride to Positano.

We agree - day trips from Positano are not workable. We were in Italy Oct to Nov 2019, traveling from Milan to Amalfi and points between. Used only public transport and "shanks mare". We found Sorrento a great place to visit. Loved our 2 night stay at Palazzo Tasso (117 euros). Could have spent another day or 2 in Sorrento. Great food at La Fenice and Kebab Di Campa. Spent 2 nights in Positano at a very good hotel (Positano Art Hotel for 238 euros), but the restaurants were mediocre at best. Stayed in Amalfi also for 2 nights at a great small hotel (Hotel L'Antico Convitto for 172 euros). Found several good restaurants. Admittedly, we were there in late season with Positano closing up, but we feel a day trip to Positano is enough unless you are into clothes shopping. We would spend more time in Sorrento and Amalfi next trip.

For day tripping to Pompeii or Naples, another vote for Sorrento over Positano. Having been to both, we were happy we'd chosen Sorrento for our base and day-tripped Positano versus the other way around. One thing to consider is that ferry service to Positano can be cancelled on days the seas are too rough to manage docking.

From Sorrento you can get to Naples by ferry, commuter train or bus. IMHO, Pompei is best reached by dirt-cheap, bare-bones Circumvesuviana commuter train; it has a station (Pompei Scavi - Villa dei Misteri) directly in front of the main entrance (Porta Marina.)

A note on the commuter train: if it continues to run, there is a tourist line of the Circumvesuviana - the Campania Express - that operates 4 times daily during high and shoulder seasons and makes fewer stops. This is a little nicer train than the regular Circ., costs a little bit more, and its limited operation is a drawback but some folks prefer it. This was the schedule for this past year:

https://www.sorrentoinsider.com/en/campania-express-train-schedule

And the 2020 schedule/other info for the Circ. just in case you want to bookmark it for next year:
https://www.sorrentoinsider.com/en/naples-to-sorrento-train-schedule

If intent on staying in Positano, some options for travel to/from Naples are explained here:
https://www.positano.com/en/how-to-get-here#section-getting-here-01

Hey guys, great responses, you've sold me on Sorrento. So, now that it's Sorrento, can you recommend some SITES and RESTAURANTS and or EXPERIENCES in the immediate and surrounding area, that you enjoyed. Larry42 mentioned La Fenice and Kebab di Campa in Sorrento. We will be staying a week so will have many opportunities to experience the local wine and foods.

We like wine tasting, eating freshly made Mozzarella di Buffala (will be looking for a local farm that offers it), Granita drinks, museums, short to medium hikes, walking tours in the city (local guide recommendations welcome) and must do's or must see's in Naples and or Pompeii / Herculenium (echoing or other than what Rick suggests in his Naples tour book) Really, I'd like to hear what your favorite thing about the area was.. Thanks,

steve

For a hotel, https://ilnido.it/ is where we stayed. Check out their webcam. The view is really better.

Excellent breakfast bar with a veranda that looks out to what is seen on the webcam.

Happily go there again.

Hotel: Antiche Mura. No coastal views but impeccable service and cool, green lawn space with pool and poolside bar: great for kicking back with a drink after a day of tramping Pompeii in the heat (plenty warm even in early October!) As most of our time was spent out and about, we had plenty of opportunities to take in the views of the bay. It's just a couple of blocks from Piazza Tasso and easy walks to the train station, restaurants, shopping, etc. but was just far enough to be quiet. Lovely breakfast room and terrace! For the extra elbow room, I would recommend springing for a "Comfort" room or better if at all possible.

https://hotelantichemura.com

https://www.tripadvisor.com/Hotel_Review-g187782-d308082-Reviews-Antiche_Mura_Hotel-Sorrento_Province_of_Naples_Campania.html

https://www.booking.com/hotel/it/nessunaantichemura.html

Get yourself some gelato and amble over to Villa Comunale at sunset to watch the lights twinkle on all around the bay.
https://www.sorrentoreview.com/villa-comunale-park.html

A self-guided walking tour (Villa Comunale is included in this itinerary):
https://www.sorrentoinsider.com/en/e/sorrento-tour-walking-itinerary

We also stayed on Capri for 2 nights and can recommend some of the hiking there. Specifically, the ramble up to Villa Jovis, and to Piazzolungo/Natural Arch. In Anacapri, the chairlift up to the top Mt Solaro is fun, and the view is terrific. You can hike down mountain if feeling ambitious? No tours needed to explore the island nor would I recommend them as you'll be more nimble on your own. The Capri town and Anacapri piazzas are usually very busy with day trippers so trekkers can find some breathing room by exploring away from them. I personally wouldn't recommend the Blue Grotto: eats too much time and hasn't been a stellar experience for too many visitors for too many reasons.

https://www.capri.com/en/traveller-search?todo%5B%5D=nature&all=1

Naples:
If you're going to Pompeii and Herculaneum, you'll want to hit the archeological museum for sure.
http://www.museoarcheologiconapoli.it/en/

Just for starters... :O)

Two things you must experience (can't avoid them) in Sorrento: lemon stuff and intarsio (wood or marble inlay work). Lemon foods, drinks and objects are everywhere. There are many shops with intarsio along with a museum and the Cathedral. The passeggiata on Corso Italia and the shopping along Via San Cesareo are great evening activities. Sorrento is a good strolling town with ocean views, old sites and a meandering network of streets & alleys.

A day trip to Positano starts with a bus near the train station. You can get off at the first bus stop at the Sorrento side of town and catch a nearby shuttle bus down to the main town. Or hike down narrow stairs and walks to see where the 'natives' live. Positano had some nice shops with clothes and touristy stuff. The wife loves the pottery but this time only pix of it going home! To return to Sorrento, just take the shuttle (the shuttle runs on a one way loop) back up your original stop and transfer to the SITE bus heading west.
We really enjoyed Amalfi & Ravello, but they really warrant a stay - too far for a day trip.

We like wine tasting, eating freshly made Mozzarella di Buffala (will be looking for a local farm that offers it), Granita drinks, museums, short to medium hikes, walking tours in the city (local guide recommendations welcome) and must do's or must see's in Naples and or Pompeii / Herculenium

There really aren't sights in Sorrento. It's good for lolling around and well-positioned for day trips. Figure it will take an hour or more each way for day trips, door-to-door. Naples has a lot to offer, most notably the National Archaeology Museum. The museum is easily combined with a visit to Herculaneum if you have the stamina. How much time you spend in Pompeii depends on how much interest you have. Some folks find 2 hours is enough, others enjoy a full day there. I'd allow a full day to explore Naples, without the museum. The RS self-guided walk is very good and will take the better part of a day if you visit the sites along the way. I haven't been to Capri, but I've been told there's pleasant hiking if you avoid the touristy places. For me, the most enjoyable thing on the Amalfi Coast is its natural beauty. The villages are not as quaint or as charming as in most other parts of the country, but the views are wonderful. The best place for pastries (to die for) is Sal de Riso in Maiori.

During high and shoulder seasons, Positano can also be reached by jetboat/high-speed ferry (abt 40 minutes one way) as long as conditions are favorable, which is more versus less often. Amalfi can be reached by jetboat/high-speed ferry in abt. 1 hour, one way. Some visitors like to go by sea one way, and back by bus.

Schedules aren't currently available as the boats don't run to Positano or Amalfi in winter; check them closer to your dates of stay in the region. The boats do cost more than the buses so may need to be budgeted for if closely watching the pennies! Due to dense traffic on the narrow coastal road and scarcity of parking, I think most of us would discourage driving yourself for a stay in the fall.

One of my favorite experiences of staying in Sorrento was renting a mini-bike to visit Amalfi-Positano area. Cheap, easy to use, great for parking and pulling off the road wherever the view looked good. Much rather ride a minibike than a car along the amalfi coast. Several places in Sorrento rented them--100cc I think.

Ok k2
You got me interested. What are the logistics of renting a scooter?
License requirements? Cost?
Can two people ride the scooter?
Helmet - separate cost?
Deposits? NZT still applies for scooters?
So many questions.....

We stayed in sorrento at pallazo tasso. Sorrento is a lovely town, very convenient for day trips to,positano( bus one way and ferry on return trip) ,capri ( ferry) and Pompeii (train) . Lots of eating options and more affordable than positano.