Normally staying somewhere only one night seems disruptive to me. But for our recent visit to the Amalfi Coast we did one night in Capri and I highly recommend it. Once the last ferry left at 6 p.m., the island's character completely changed. In Anacapri especially, the locals came out. The square and restaurants were full of people speaking Italian, rather than Americans everywhere. We saw a big church procession complete with costumes, statues, etc. It got much quieter and more fun to ride the scooter.
Our formula was 2 nights in Sorrento, 1 in Capri, 2 in Praiano. Brooke Shields walked passed us on the sidewalk when we were out for a stroll in Praiano, an absolutely charming seaside town between Positano and Amalfi that hasn't been completely overrun yet and still felt Italian. If you go, the lovely Hotel Margherita has a pool with a view that goes on forever, free shuttle van to the uncrowded beach at Marina di Praia, and a funny little electric Twizy cart for 2 you can rent that will get you to Ravello and back no problem.