There are several possibilities to get to Cortona:
Arriving by car: If you arrive by car, both from the North and from the South, take the Valdichiana exit from the A1 highway, which is called Autostrada del Sole. Right after the toll gate exit take the E45 freeway (slip road from Siena to Perugia) in the direction to Perugia and then take the second exit for Cortona (Cortona San Lorenzo). You will just need to follow the street signs to arrive to the SS71 road in Camucia and to continue to Cortona.
Arriving by plane:
1. Fly to Florence and then take a train from Florence to Camucia-Cortona. From Florence airport, you can take the subway linea T2 to Florence train station S. Maria Novella (20 minutes), and then a direct train to Cortona (1h30).
2. Fly to Perugia and then take a train from Perugia to Camucia-Cortona (the train takes approximately 45min).
3. Fly to Rome and then take a train from Rome to Camucia-Cortona. From Rome Fiumicino airport you can take a train to Roma Tiburtina and then another train to Cortona (about 3h total).
From the train station to the city center - by taxi
Next, to go from one of Cortona's train stations to either the city center or to Palazzone the easiest thing is to take a taxi. Please be aware that on Sunday could be complicated to find a taxi outside of the station. You should book it on the phone. A list of numbers that you can call to book one is here:
ADREANI Enzo: +39 335 8196313
BELLERI Enzo: +39 335 335394
CALERI Albino: +39 368 7386544 // +39 338 7043596
NAKA Ylli: +39 328 5443970
OLIVI Francesco: +39 391 4239606 // +39 335 1256420
PRVULOVIC Dejan/Miki: +39 348 4023501 // +39 338 9317508
SALIJEVIC Saban: +39 338 2877210
SEMBOLINI Gian Enrico: +39 338 5331155
VINCIARELLI Enzo: +39 335 6050186
VALVARITO Vito: +39 339 3774976
From the train station to the city center - by bus
If you want to avoid the taxi, there are several busses going from both stations to the center of Cortona. You can use the travel planner of Autolinee Toscane (link) to find a bus: insert on of the two stations in Departure and "Cortona" (green icon) in arrival.