Nearest train station: Termoli or Vasto. A car can be rented in or around both stations.
Nearest ferry port: Termoli
Nearest airport: Pescara
Pescara Airport : Ryanair currently have two daily scheduled flights from Stanstead. You can book and hire a car with Hertz (through Ryanair) and drive to Villa Masseria in around 45 minutes.
Ancona Airport : You could get a flight from Stanstead into Ancona. From there it is a 2hr scenic drive to the Villa.
Roma Fiumicino Airport: 3hrs drive.