The two major cities we recommend flying into are Rome or Florence. The major airport in Rome is Fiumicino (FCO) and the major airport in Florence is Peretola (FLR). Rome has direct flights from Miami via ITA Airways, while flights to Florence will have at least 1 layover.
Download "Trainline" in the app store (green logo and 9k reviews) The stop will be Camucia-Cortona. The main train station in Rome is Roma Termini, and the main train station in Florence is Firenze Santa Maria Novella. Book from these stations to Camucia-Cortona.
$15-$25
Train to Cortona (Camucia-Cortona) from Rome (Roma Termini) is 2 hours 20 minutes and the train from Florence (Firenze Santa Maria Novella) is 1 hour 20 minutes.