We'll be based in Cortona and rather than taking numerous day trips I'm thinking about taking the train for an overnight in Florence then the train again to an overnight in Venice and then returning to Cortona. Does this make sense? Also, should we consider a boat trip from Venice to somewhere on the coast where we could catch a train for the return to Cortona?
It makes a lot of sense to me. Florence is an easy day trip by train, an hour or so each way, so it is not really necessary to stay the night unless you just want to do that. One year we stayed two weeks in Cortona and I took a weekend trip to Venice to meet my sister and some girlfriends. The train station is right in Venice so you don't have to leave Venice to catch the train. The train trip between Venice and Cortona takes about 4 hours, and I had to change trains in Florence. I used a travel agent in Cortona to book my train tickets between Cortona and Venice. For Florence, I just buy my tickets at the train station on the day I am traveling.
Just a note that there is no train station in Cortona. However, there are frequent bus runs to the nearest train station. From the Camucia train station, it is a 90 minute train journey to Florence. It's an hour the other way to Assisi if you wish to visit there. For Venice, the train journey is 4hrs 10min from the Camucia train station. All runs will take you to Florence first where you will then change trains to a high-speed to Venice. An overnight will work well for this journey.
Thanks so much for sharing your knowledge of the area.