Parking in Cortona

I understand your pain. We managed to snag one of the last spaces on SP34 on the north side near Porta Colonia on a late weekday morning in October. The best advice may be to get up crazy early to arrive before the hordes or late in the day.

I've never had problem finding parking at this lot, but maybe you went during an especially busy period.
https://goo.gl/maps/8y7BgbjpDdArowHY8

If everything is taken there (and elsewhere, since there are several lots), you will certainly find it here, near the Girifalco Fortress.
https://goo.gl/maps/kfV5onTfEzCEjYxr6
From there to the town center is downhill, but then to get back to the car it will be a steep uphill walk, so if you have mobility issues (or are very unfit), don't park here. The parking is perfect if you want to visit the fortress but don't want to walk uphill all the way from the town center.

We stayed 3 nights in Cortona last week, although had no car. We arrived via the Terontola-Cortona station and took a bus up to the walled town from there, and took a bus down to the Camucia Cortona station for our departure. The exterior lots outside the wall gates I saw did seem to have at least a few open spaces (maybe that’s October), but taking the bus to/from the train stations for €1.50 each way was simple. We had to put our carry-on suitcases on the seats, as suggested by our arrival bus driver, and hold on to them upon heading downhill on our departure, on a bigger bus, where putting them on the seat just didn’t seem right. It takes several minutes to reach the walled town from either station, but if parking there is easier or more ample, go for it. Is the parking at the station any cheaper, though?

I assume that there would be paid parking either at the Cortona lots or the train station lots, not looking to compare parking rates, just interested in other's experiences parking at one of the train stations and making their way to / from the old city center.

Using Google Maps Street View, I can see that the Terontola-Cortona station lot has blue lines indicating paid parking, while the Camucia Cortona station (much larger) lot doesn't have any lines, so maybe parking is free there, didn't actually look at Parking signs. But convenience and availability is more of a concern than paying for parking.

We were there last week for three nights, and as Cyn said, the bus is easy. You buy the tickets at the little store/restaurant just outside the station, go to the bus stop right there and wait for the next bus. They drop you off at the top of Piazza Garibaldi, and from there you are steps away from the center of town. We never found taxis waiting at the station. We did use a taxi to take us to the train station on our departure day, and one other time. They also will meet you at Piazza Garibaldi and take you down the hill. They charged 20 Euro for the trip each way. Pricey? Yes, but it worked for the three of us and was very convenient. The bus is much cheaper and does run regularly but less of a schedule on Sundays. The tourist office has a list of parking lots as well as a list of taxi drivers you can call or make pre-arrangements. We used this list to secure a taxi when we needed it. They also have bus schedules. The parking lots were quite full when we were there, but as someone said, on occasion, there were open spots. We did a day trip to Montepulciano/Pienza while there. We did not have a car in Cortona, as having been there before, knew it could be a hindrance. We took the train to Chiusi, rented a car from Budget for the day, and visited towns before returning the car in the afternoon for the train trip back to Cortona. A private driver wanted $350 US, and we found our option much cheaper.