We will be on a cruise in July and have a stop at Naples. We've previously been to Naples and Pompeii, and wanted to go to one or some combination of Capri, Sorrento, and Positano. The ship offers a couple of excursions that visit Sorrento and Capri or Positano and Capri, the latter is a more expensive photography excursion. If we were to do Capri then Sorrento, I think I could feasibly get hydrofoil tickets in advance and do that on our own, or maybe consider the excursion. Positano seems more out of the way, so would likely go with the ship excursion to make sure the timing works out. We're not fully against spending the day in one place, but since we have limited time, if its feasible, we'd like to see 2 of those places if possible, understanding it wont do these places justice and would be a bit rushed. Wanted to get feedback from anyone who has done one of these combos on a port day in Naples, thanks!
Because of distances involved and transportation it would be hard to see two in one day. Capri is a full day in itself. I would also use the ship excursion for Capri. Sometimes late pm storms on the bay will disrupt hydrofoil travel. If you are with a ship's excursion they will wait for your return. If independent, the ship doesn't wait. You could take the train to Sorrento and return via ferry to your ship. The ship's excursions has some advantages at this port.
I don’t feel like there’s a huge upside trying to do Sorrento-Capri on your own. Or I’d at least use the ship excursion for the transportation and ditch the guided tour once ashore. Sorrento is basically a stopover either way, there’s not much to see. This excursion is really about Capri.
The Capri-Positano excursion… you could justify a splurge here I think. That’s two highlight-reel destinations in a day that you definitely couldn’t pull off on your own.
I agree with previous replies that it would be a good idea to use the ship's excursions in this case, due to the distances and transportation involved. If you do that on your own and miss departure, it will be an expensive and annoying holiday experience!
With the options you listed I'd probably choose Positano - Capri, as that will meet your goal of seeing two of the places and will allow a brief look in case you want to return for a longer visit in future.
In addition to the wise advice already to use the ship excursion, I'd point out that Capri is a huge destination, very spread out, hilly, and highly pedestrian-only. This may be a case (i.e. very limited time) where a (gasp!) regimented tour with no individual decision making is a plus. You have to deal with the facts, not a gauzy dream of Capri.
We just spent a day in Capri on May 7th and let me tell you it was crowded. I was shocked to see how many people were there and I can't imagine going there in the middle of the summer with the heat and even larger crowds. My niece just spent the morning and Positano on May 8th to have pictures taken with her husband. They are doing work on the dock and there and are late completing the work. I don't know when the dock work will be completed, but my niece couldn't get on a ferry back to Sorento and had to take a taxi back for 50 euro. If for some reason they don't complete the new dock work by this summer I can't even imagine what will be like when the crowds thicken and the heat sets in. Sorrento is nice with a lot of restaurants and shopping, so if I was going to do a day trip, and knowing what I know now, I would go to Sorrento. Plus you have more options to get there, i.e. ferry, Campania Express or cab. Tip - don't take the commuter Circumvesuviana train. It's unreliable, very crowded reminds me of the old New York City subway trains from the '70s and '80s with all the graffiti.
As for Summer in Italy, it is no worse than Summer in South Georgia where I live. I have no problem visiting Italy in the Summer.
Having been to all three, I would go with Sorrento and Capri.
I have fond memories of going in the Blue Grotto near Capri and my boatman singing O Sola Mia.