I just got back from my trip and spent 3 days in Cinque Terre and Levanto.
Here is some excellent advice that I could not find when I was on my actual trip because my internet connections were often slow and I wanted to spend time enjoying my trip instead of waiting for pages to download. However, I should have printed off this schedule and info before I left.
This was some helpful advice I got from Robert here on the RS forums when I asked about avoiding crowds in Cinque Terre.
A prior crusie post had this website to check which ships are in which port on different days. Some ports close by that day trippers may use. I Picked July 14 but you can change the month and see all the ships in port
http://ports.cruisett.com/schedule/Italy/1083-La_Spezia/July_2014/
http://ports.cruisett.com/schedule/Italy/210-Florence_Livorno/July_2014/
http://ports.cruisett.com/schedule/Italy/368-La_Spezia_cinque_Terre/July_2014/
Trust me when I say...you want to avoid Cinque Terre on cruise ship days or do what I did and go VERY early morning or maybe in the evening. I happened to go my first day on a cruise ship day and it was so crowded on the trains between towns that people were wedged in the doorways and often would not let others ON the train. The next day was SO MUCH better!
So...take it from a now-experienced Cinque Terre "newbie." :-) Enjoy your trip...it is captivating and gorgeous.