Boat day trips from Naples

Also look at taking train to Salerno, then ferry hopping from there. It will be a contest of budget vs convenience. Travelmar is the Amalfi Coast ferry.

Note that (in Sorrento anyway) there is more than one ferry company. The only reason that matters is that the one you buy a ticket from will not tell you that you could leave for Capri a half-hour sooner at the other company! Especially from Naples, an all-water AC tour could be pricey. I personally think you can see how beautiful Positano is from the beach, and you don't need a boat-ride. I'd rather have the time to take a bus to Ravello and view down. Opinion.

By the end of May, traffic will be heavy, and you will need to buy your return ferry ticket at the same time as your departure. Because you won't have luggage, the gritty and jammed Circumvesuviana train is simply like rush hour in a big city. Perfect access to Pompeii, Herculaneum, and Sorrento.

In late May, the public (SITA) busses between Amalfi and Sorrento are very crowded, with lines that exceed the capacity of the next, half-hourly, bus. As another posted, it's budget versus speed and comfort. Because we were sleeping in Sorrento, we hired a car and driver (not really "a guide") for 8 hours to see the AC. But that's a high-ticket luxury.

What you probably want is the boat ride (ferry or tour) from Sorrento to Amalfi - that's where the great scenery is. The boat from Naples to Sorrento is across the large bay so the scenery is not that great. I think the best option would be to get to Sorrento from Naples (either by boat or train) and then get the ferry to Amalfi - probably stopping at Positano. But you will need to research the times to make it work. I have done several day trips from a base in Sorrento, taking an (approximately) 9:30 ferry, stopping at Positano, then to Amalfi and then an (approximately) 4:30 reverse back down to Sorrento. Gives you enough time to explore Positano and Amalfi and even to take a bus up to Ravello. But the ferries don't run all that often so you'd need to know the times.

What are your plans for a week in Naples. Perhaps you could split the time and spend a few nights in Sorrento to make the day trip easier, and Sorrento itself is a great town.

Here's a photo of Positano taken from the ferry heading down to Amalfi. The rest of the photos in that gallery of the Amalfi coast I mostly took from the bus between Sorrento and Positano/Amalfi which also afford wonderful views but is not as much fun as the boat

https://andiamo.zenfolio.com/p266655284

The photo I'm talking about is number 93. They are numbered so just scroll down.

The thing you need to be aware of is many of the ferries do not allow you to sit outside. We took a ferry to Sorrento from Naples and one from Capri to Naples that were more like being on a plane than a ferry. It really was transportation and nothing more.

We also took a ferry along the Amalfi coast that had gorgeous views and one from Positano to Capri that was pleasant but not as beautiful. Both of these were smaller boats with seats outside.

I've never taken a private boat view-tour as the OP wants. But (individual operators aside) it tends to be a luxury product. It's also unreasonable to expect a tiny boat with open decks to start at Naples and go on open water all the way to the AC. There are exceptions, but the bigger the boat, the more likely you are to be inside, behind a window.

I agree about "like an airline." One of our Sorrento-Capri ferries was 200+ literal airline-seats in a blessedly air conditioned cabin with little or no viewports. The return ferry (Capri-Sorrento) was a little more traditional, but standing room only, at 5:30PM. We actually went out on the "rear" open deck to get away from the stuffy interior. But it was like the rear deck of a Hoboken Ferry in 1960: Steel roof above, car deck (inaccessible) below, faint diesel odor, welcome bottle of beer bought at the bar before going outside.

Interesting sidelight, the return ferry left from a dock 0.25 mile away from the dock we arrived at. (Same Capri harbor, certainly.) Be sure to look on a departures signboard (in the few BIG ports) before walking "to" your ferry.

Thank you everyone for replying to my question, this has helped a great deal. Now we are thinking of taking an early train to Sorrento, taking a small group boat tour of the AC, spending the night in Sorrento and then taking a ferry back to Naples. Does this sound doable?