The no-car question is not simply whether a town has a station. It is whether the trip still works after arrival, luggage, old-town access, beach movement, dinner timing, and late returns are added to the plan.
That is why the safest answer starts with places that can carry the practical parts of the route. Bari is the gateway tool, Monopoli is the strongest coast-first stay, Polignano is a focused cliff-town choice, and Lecce is the cleanest city stay when Salento truly belongs in the trip.
Everything else can still be worthwhile. Locorotondo, Martina Franca, Ostuni, Alberobello, Matera, lidos, masserie, wineries, and countryside dinners just need more proof before they become no-car overnight decisions.