We flew into Faro and took the regional bus west. Lagos makes a good base: the Ponta da Piedade trail starts a short walk from the old town.
Day two was the Seven Hanging Valleys trail — go early, take water, and finish with grilled sardines in Carvoeiro.
Trains from Bari reach Monopoli and Polignano in under an hour. Alberobello is busy at noon and quiet after five.