I'd like to visit Monopoli while I'm in Italy. I will be staying in Rome, Florence and Venice. Where is the best point in my travels to take a side trip to Monopoli and how best to get there?
Rome, but it is about a 5 hour train trip.
None !!! Have you looked on a map? Roughly speaking it will be 9/10 hours from Venice, 8/9 hours from Florence but only about 5 hours from Rome. Each route is at least one train change. So Rome is the closest but really not a good day trip from Rome.
I visited Monopoli last year, not as interesting as I had expected. We were staying in Matera at the time. Will you be driving? Public transportation from Roma to the archeological site will be challenging.