If it's you're only option (including any future possible trips) to see Florence, I would go. It's much smaller than Rome and beautiful. [When DD17 wanted to see Paris--it was 3 hours on tour bus each way. We had only a whirlwind 4 hours to (literally) run around Paris, but she loved it.]
Florence can be a very enjoyable walk-about with out even having any museums, etc. reserved for 4-6 hours. Viewing the outside of the Duomo (esp the bronze door scenes), walking by the "fake" David in the square, walking over the bridge, stopping at a cafe for a snack/drink, and meandering down the little side streets doing some leather shopping is a wonderful day.
With that said, Cinque Terre is one of the most beautiful areas in the world-small cliffside villages in an incredible setting. It's very close to La Spezia.