2 and half weeks Italy Itinerary

Hello, my spouse and I are planning a 2 and half week Italy trip next May and are having a hard time narrowing down our itinerary. Our plan was to fly into Rome and out of Florence if possible. So far we have a tentative list of the places we would like to visit. It's as follows:

• Rome - 4 days
• Sorrento - 3 days, day trips to Capri and Amalfi
• Tuscany (Sienna), 3 days
• Cinque Terre - 2 days
• Lake Cuomo - 1-2 days, unsure
• Florence - 3 days.

I realize this is a lot for only 2 and a half weeks so I'm unsure of what to narrow down and what to add.
We don't want to spend half our time travelling but we do want to see what places we can in the time allotted. The days above are not including the days we fly into Rome and out of Florence, so they are all full days. How would you allocate the time allotted for the places we'd like to see? are there any we should cut out? Thanks in advance!