I think we want to do 2 days in Cinque Terra for sure, and we'd like to see Rome. Do we have time for anything in the North? If so, what do you recommend? Thanks!
CT and Rome are a looooong ways apart. It will take you about 6 hours or more to travel from one to the other by car or train. Plus, where are you flying in and out of? Wouldn't you rather spend that time another way? I think you should choose to either spend all the time in Rome (side trip to Pompeii) or stay up north spending 2 days in CT, (stop in Pisa on the train between CT and Florence), 2-3 days in Florence and, if there's time, add one day trip to Tuscany (Montepulciano, San Gimignano, or Siena) from Florence.
Visiting a friend in London, so no plans for method of travel to Italy yet, but flying out of Rome.
From London, fly into Pisa and take train to CT. Leave early in the morning from CT to get to Rome by midday. It is doable but you do not have time for anything else.
If you start by spending 2 full days in CT, you won't be in Rome until after 2pm on the 3rd day if you look up the connection on the trenitalia site. And that's getting on the 8am train. So my suggestion is to spend the remaining days in Rome.