I’m looking for a map to determine how close the train station is to the Centro Storico in each town. Would it be easy to travel by train to one of these towns for a few hours touring, have dinner and head back to Bari in the evening?
Sure! Just go to Google Maps and zoom in (search for "station if all else fails--I just follow the tracks when I need confirmation), I believe in both of those towns the train station is a short walk (not always the case in Puglia). In Bari, it's about a 15 minute walk.
With Bari being such a great dining city, not sure I'd spend the time on the train, but it's "doable" as they say.
We stayed in Monopoli and did daytrips to Polignano and Bari. Even though we did have a car, we used the train for both. Super easy, no parking issues. I'd say the train stations in those towns are about .9 to 1 mile from city center and an easy flat walk with sidewalks.
Have you heard about Assassin's Pasta? (See Stanley Tucci or Pasta Queen shows). Really yummy, unusual and first served in Bari. Depending on when you are traveling and the time you like to dine, you might consider a reservation. I believe the restaurant was called Urban and it was between the train station and the old town. HIGHLY recommend