Honeymoon: 1 month in Southern Italy?

We would like to go to the Amalfi Coast for our honeymoon. I once spent a month in Florence, and besides a few day trips, had so much fun exploring the city. I could spend hours on each street. I thought it would be fun to have an experience like that on the Amalfi Coast. Would you recommend staying in one place there, and exploring the different islands and towns for a month? Or would it better to stay in a different place each week, all on the coast. Such as Positano one week, Sorrento another. Just to get a real feel for the place. Open to suggestions...