What hotels offer four star minimum quality? Would like something central to the shops within walking distance and an elevator needed in the hotel. Any recommendations?

Try the Palazzo Murat right in the centre near the bus terminal and at the top of the path to the beach.

Does your request for an elevator denote some walking difficulty, at least with steps? If so, be aware that Positano is very steep and has lots of wide steps down to the beach through the shops etc.

we have a stroller actually so an elevator is essential for our positano hotel. The Eden Roc and Covo seem nice?

We couldn't find availability in Positano to suit our needs, so anyone suggest Ravello or Amalfi? Any comments on best hotels and best shopping, etc?

Did you look at Buca di Bacco.