I just got back from this very region.
Naples was too dirty and gritty for my taste. I'm glad we had just one night there.
Positano was stunning. But know this: you must climb up and down hill on foot. There is only one lateral, mostly horizontal road. It leads one way through town. This is not a town for the faint of calves. Many, but not all hotels are on this road. We stayed at the Hotel Califronia. Absolutely charming. Phenomenal views of the town and ocean. Excellent small restaurant at the hotel too with views.
BRAND NEW HIDDEN GEM: In Positano you must go to Mar Positano. This is a museum under the main church in town. These are archaeological ruins which opened to the public only 6 months ago in the summer of 2018! Access is "brand new" but what you'll see dates back to the era of Mount Vesuvius' explosion. The church under the church and all its wall paintings were buried. That preserved them. The colors seem as bright as they were when they were painted. You'll also see rows of special "chairs" where archaeologists found the remains of mummified priests. (Their remains are gone now, whew.) Amazing, fascinating place.
Advice from a friend who visited there recently and from a local warned us about unreliability of the local buses leading farther up the Amalfi coast. So we opted instead for the ferry for a day trip to Amalfi and back. That worked out just fine. The paper museum in Amalfi is interesting, but the English of guides varies. The woman who leads tours is very understandable. The man who led us was impossible to understand. They still make paper on the site and sell handmade papers and cards.
We also hired driver Francesco del Pizzo recommended in Rick Steve's Italy book to drive us from Naples to Positano with stops at Herculaneum and Pompeii en route. This was a great move. The driver was very friendly, spoke great English and taught us so much about the Napoli region. This car service also offered a local tour guide for a personal tour at Pompeii. This was another good move. She got us in past some lines and shared so much more with us than we would have learned from an audio guide.
Beaches: I agree with others: bring water shoes. No soft sand to walk on here. Just small rocks.
While Positano was quaint and charming, Sorrento may have been a better home base.