Cortona can be reached by flying to Italian major international airports in Rome and Milan, or to the two airports in Tuscany:
Pisa International Airport Galileo GalileiIATA: PSA (http://www.pisa-airport.com/), located 1.5 km 1 mi north of Pisa city centre, served by many budget airlines. From there you can take a train 40 metres from airport.
Florence Airport Amerigo VespucciIATA:FLR (http://www.airport.floren...), Located four kilometres from the centre of Florence. From there you can use the Sita/Ataf service "Fly by Bus" Vola in bus between the airport and Florence's Santa Maria Novella railway station 20 min.
Closest train station is "Camucia-Cortona", with direct trains from Florence and Rome or "Terontola-Cortona" with direct trains from Florence and Venice. You can also take a train to Arezzo and then another train to "Camucia-Cortona". A bus is leaving every 30 min from the Camucia station to town. Taxi is available in front of the Camucia station and Terontola train station however apparently there are only few taxi serving this "route". If you want to be sure that there is taxi for you, ask your hotel to book one for you. The other option could be rent a car and you can do it right outside of Terontola-Cortona train station and use your car to reach your destinations.
Take the Autostrada del Sole highway A1, exit at the Valdichiana toll-gate and get on the Siena-Perugia speedway, direction Perugia. Get off the speedway at the Cortona-San Lorenzo exit. Keep driving direction Cortona, drive past Camucia and follow signs for Cortona. Climbing up the hill, you will find the Cortona town-limit sign.