The small piazza wrapped around the seaward side of the Castello di Carlo V is the prettiest spot in Monopoli for an aperitivo. The square sits a few metres above the water with a low stone parapet and views straight out into the Adriatic; the rocks at the foot of the castle wall are a favourite jumping-in spot for local teenagers in summer.
In the evenings the square fills with people taking a slow drink before dinner. Two or three of the cafes have outdoor tables here; the prices are a euro or two above the rest of the town, but you are paying for the view.