I'll be staying with a friend in Cortona for 3 days and plan to make day trips to nearby sites. What would be the best way to get to Cinque Terre and back in 1 day?
you can't do this too easily. Its around 5 hours each way by train, and there's limited parking assuming you decided to rent a car and drive.
I wish I had better news for you: The fastest trains take 5 hours each way, that's a round trip of 10 hours. And to the 10 hours you must add the time to get to the train station and wait for the train at both ends. So you're looking at 11 to 12 hours of seeing the inside of several trains (there are train changes required) and train stations.
Just got back from Italy. I was both close to cortona and in CT amongst other places. The advice from the other posting is good. And if your intent is just to go out and see, you would be better off just buying a post card. The experience of CT is from being there, walking the trails etc. And where you are going to be is every bit as beautiful and full of things to do.