I LOVE SORRENTO! I always stay at il Nido (ilnido.it) which is above the town. IMHO they have the best food in Sorrento for both breakfast and dinner. Dinner on the veranda, overlooking the entire Bay of Naples - it doesn't get more romantic than that!!! 3 nights isn't bad. You could squeeze in a daytrip around the Amalfi Coast, and either Capri or Pompeii. That's leaving you very little time for Sorrento itself - remember you have to arrive/unpack and then pack/leave so you really aren't there very long. If you like pottery, Sorrento has some amazing colors in their ceramics. My passion though is their linen shirts (after over 12 years my closet is more than full!).
Can you consider staying in Siena and day tripping to Florence? It's easy by bus. Siena, for my partner and I, is much more interesting at night than Florence. I'd then cut some time and add it to Rome, which itself could fill your two weeks. Lucca is a beautiful city. I just saw that it is on your list so here's another suggestion for your planning: stay in Florence and day trip to Lucca (by train) and Siena (by bus). Florence becomes, for me, a better home base. But again, you could shave some time and give it to Rome.
Where are you flying from? Naples and Pisa may be convenient in some respects but expensive in others.
You'll be getting lots of suggestions - people on this forum are full of excellent ones! Give us more information (likes, must dos, less interested in) and we'll all be glad to help you with planning, which is a great part of the trip itself!