Monopoli (56 km away)
Monopoli is a port city much less touristy than Lecce or Alberobello but still worth a visit. Thus preserved from mass tourism, Monopoli is an authentic Italian town with a picturesque seafront promenade. In the center there are many bars, cafes and restaurants with good value for money.
The port is connected to the historic center by a large window that allows for great photos. There's even a beach in town and the best part is that it's not crowded in August!
To see: Charles V castle, cathedral rebuilt in the eighteenth century in baroque style, ospedale Gerosolomitano etc.