3 days in Capri and 3 days in Positano.

Steve,

You might find some good suggestions in the RS Italy guidebook. I don't recall there being many activities in Positano other than beach time or shopping, although you could take day trips (by bus) from there to other locations. One possibility would be to travel to Sorrento by bus or taxi, and then take the train to visit Pompeii. Seeing the site with a guide would be best, as you'll learn far more about the history.

On Capri you could visit the famous Blue Grotto but I've never bothered as it didn't interest me. There are a lot of posh stores there such as Prada, Gucci, D&G, etc. so if you want to spend money, that's a good place to do it. You could travel to Anacapri and have a look there. Other ideas in the guidebooks.

Thanks for your reply. We do have the RS guide. I know the beauty, the beach, and the shopping, and hopefully the food are the main attractions. Have also been told there are some nice hikes. We are active seniors but don’t want to overdo it. Any other thoughts would be appreciated.

There are several more towns along the Amalfi Coast that most are not aware of or don't visit.

https://www.amalficoast.com

Take the bus to Amalfi and up to Ravello.
Hike down to Atrani and walk into Amalfi.
Then take the ferry home from Amalfi.
Ravello-enjoy Mama Agata's cooking class
Hike the Path of the Gods - just spectacular views and the highlight of our Coast trip. We took the bus from Positano up to Nocelle and followed the signs
Capri - hike to Arco Naturale and walk the Via Krupp Augustus gardens

Capri: hike Villa Jovis and Pizzolungo, and take the chairlift in Anacapri up to the top of Mt. Solaro:
(Ignore the ad for tours; you don't need them).

https://www.capri.net/en/s/villa-jovis-mount-tiberio
https://www.capri.net/en/s/arco-naturale-and-pizzolungo
https://www.capri.net/en/s/mount-solaro-cetrella

If there's a tourist trap on Capri, it's the Blue Grotto. Personally, I'd give it a skip.
Both Capri and Positano are high-end tourist destinations a bit light on "local" flavor. If looking for restaurants the Capri islanders might go to, your best bets are probably the few which stay open in the winter. They're most likely to be frequented by the locals during both high and low seasons

https://www.capri.net/en/e/budget-restaurants-capri
https://www.capri.net/en/e/bite-size-guide-to-the-island-in-winter

In Positano, go to Franco’s for a before dinner drink! You won’t regret it. Them walk right up the street a block or less to Bar Bruno and eat outside next to the rail. Make a reservation. But you better be at Franco’s at opening. It’s limited seating and fills very quickly.

Thanks for the many great suggestions. We will be there in late May and looking forward to it.

I found many more things to do on Capri than there are in Positano. Both places are HIGHLY PEDESTRIANIZED and filled with hills and steps. You have no alternative to physical exertion, just to go to the beach or out to dinner. I personally got tired of the same Euro-luxury boutiques that you can see anywhere in the world. So shopping was not very satisfying for me.

In exchange for money, you can hire a car and driver in Positano, but traffic is awful on the only road through the town. Even Pompeii is over an hour from Positano, so it's not a "daytrip" location, it's a beach location. There is a bus line that runs from Sorrento to Amalfi, through Positano. But that is also very crowded, and subject to road delays.

In Positano, dinner at La Tagliata.. one of the highlights of our trip! They pick you up at your hotel and take you to their restaurant. Her sons pour wine and mama cooks a full meal for you! Very reasonable price and fun atmosphere with others!

Dinners on Capri:
Ristorante Il Geranio, sit outside, views are beautiful, food very good.
Da Giorgio, in town, go at night to avoid crowded area, traditional Italian, very good
Ristorante Monzu, at Punta Tragara, some of the best foods we have ever eaten!

I don’t think anyone has yet mentioned the church of San Michele in Anacapri, with its fantastic ceramic tile rendering of the Garden of Eden. Also in Anacapri there is a villa with lovely gardens. In my opinion, Ravello is the most beautiful town on the A.C.
By the way, regarding beaches . . . You may be disappointed in that of Positano. As I remember, it is none too big, with grayish sand. I would probably find the water too cold in May, but I’m definitely on the wimpy side when it comes to water temps.