Bari Centrale is a bustling train station that will allow you to base yourself in Bari and easily explore central Puglia without a car. For only a few euros, you can easily get to the towns on this map - Polignano a Mare, Monopoli, and Trani. To reach Alberobello, you will have to switch trains, so I recommend using the bus instead (the bus stop is on the street behind Bari Centrale, and I recommend booking your Alberobello bus tickets in advance).