If you do leave Lo Scoglio, walk into the piazza to have a pair of sandals custom-fit at the tiny shop Il Piccolo Positano. (You can't miss it: There's only one shop.) Come before lunch, and they'll be ready by the end. The prices are better than they are in Positano, too.
Pavia is the founder of Fathom. She splits her time between New York and London, but is happiest on the Sorrentine Peninsula. You can find her on Twitter at @pavianyc. She travels for the four-hour lunches.