We took a very similar trip about 10 years ago. Stayed in Rome for 3 or 4 nights, then Florence for 2 nights, and Manarola (Cinque Terre) I believe for 2 nights. It was a bit of a whirlwind, but we had time to see all of the main attractions in each place. That included a "Tour of Tuscany" guided tour. We traveled by train a lot, and that was very convenient/efficient. In fact, the last stop on the Tour of Tuscany was Pisa, and we took a train from there to Manarola instead of returning to Florence on the bus with the rest of the tour. Great, great trip. One thing I would point out is that they have transportation strikes fairly frequently in Italy. I can't recall the exact details, but I do remember them striking while we were in the Cinque Terre, and we started exploring how we were going to make it to Civitavecchia. It ended up being that they kept major lines open, so we caught the train we originally expected to. Just want to throw that out there in case you run into a similar scare.
Also, highly recommend using Rick Steves' self-guided audio tours. They were absolutely fantastic when we were walking around Rome (as well as Florence). I believe we also used them in Athens...and possibly Ephesus and Siena (Siena was part of that Tour of Tuscany).