The walking is brilliant, up and down LOTS of steps (e.g. ~ 1200 from Ravello down to Amalfi). The Julian Tippett pcoket walking book (in the sunflower series) remains very useful. It’s not super-detailed on directions, but it’s good enough. Do however take good care if it’s wet, as those steps become treacherous.
I agree with Michael on that Valley of the Mills walk - such a lovely flow to it, and so bereft of people (a world away from the Cinque Terre conveyor belt). Still there are countless walks, with a wonderful criss-cross of old paths / mule tracks, and we’ve made other routes not covered in Tippett. Another short, simple but oddly strenuous walk, is the brief hop from Amalfi to Atrani, and it’s recommended for the unusual ‘houses in the viaduct’ architecture, but also A’Paranza seafood restaurant in Atrani
For only 3-4 days, it’s worth thinking about what is a ‘must see’ for you. Is it the Greek temples at Paestum, extensive Roman ruins at Pompeii, or the more compact Herculaneum? Or is the walking the big appeal? (for us it is). At the same time, there is a decision to be made about a car. In general I’d say don’t. The coast road is busy/gets clogged up, parking can be a nightmare, but not as much of a nightmare as the scary driving conditions on steep switchback roads. For getting around, the SITA buses are frequent and good, with highly skilled drivers who make it look easy. Plus walking can be a legitimate way to get around. Only go for the car if you really want to see Paestum, Pompeii & Herculaneum in this trip AND you and your family have no issue with scary driving landscapes.
Those thoughts should help you narrow down to a place to stay, be it:
Ravello for relaxation, stunning views and modest day trips often including a walk down and bus back up
Sorrento for ease of access by train & getting to Herculaneum/Pompeii by public transport
Positano for a pastel-scenic base (though if the ferries aren’t running you’ll miss out on the best view of the place)
Amalfi for ease of transport, to allow easy day trips to Ravello, Positano
There are other bases worth considering: Minoro, Praiano, Atrani, Scala etc.
Regards
Ian
p.s. Pasticceria Andrea Pansa in Amalfi. Should be a highlight for all the family.