Hi Phil, in 2013 i spent almost a month in Northern Italy (Rome and north). While I had a wonderful trip, i came away with two important lessons for the future: (1) Don't move from one town and hotel to another too often, especially when traveling by public transport, as each move really eats up a lot of time and energy; and (2) don't just grab any ole thing to eat only because it's time to eat, especially to eat it on the run, when there is so much great Italian food to sit and really enjoy. I think it's usually even better to go hungry a little bit, in order to enjoy a good sit-down meal a little later.
i share that, mostly just to agree with others that your initial expectations seem way, way over-stretched, and also do not allot various locations the amount of time they really deserve, some too much, some too little. Of course where you choose to ultimately visit will depend a lot on the particular interests of yourself and others in your travel group. Are your prime interests fine art and architecture, or outdoor activities, or experiencing Italian culture and history, or fine food and wine, or what?
I myself am headed back to Italy this May to focus on the south, mostly two weeks in Sicily and a week in the Naples and Amalfi Coast area.
All that said, I would suggest:
1. Leave Sicily for a future trip. It is distant, quite large, very interesting and diverse, and deserves real exploration, not just a momentary stop.
2. Cinque Terre is very nice for a couple full days, if the season is right and the weather is good. I think 5 days is too much given your other plans.
3. Venice, Florence and Rome are all wonderful, and quite different. i would suggest spending at least three full days in each.
4. i have never seen anyone else list visiting Genoa as a priority before. I've never been and would skip it unless it was on my route anyway, then I might stop to take a look.
5. The Amalfi Coast is some distance south of Rome, and travel and settling into lodging would take you at least a half day each way. Including it will require compromising in other areas.
6. Siena, Assisi and Lucca are all very nice. There are pros and cons to spending nights in these towns, as opposed to day trips. Depending on the season, day trips can put you there just when all the other daytrippers are also there, so a heavily touristic visit. Often the most magical times in these towns are the evenings and early mornings, which you miss on day trips. Of the three, I think Lucca is the most skippable.
7. You also asked for suggested additions. If you really thin out your current list of visits, you might consider Orvieto (in Umbria near Rome), San Gimignano or Volterra (both in Tuscany) all of which I really enjoyed last year, or Verona or Ravenna (a little out of the way), which i will be visiting this May. Also for scenery and outdoor activities, the Dolomites and the various northern Italian lakes offer a lot to see and experience, depending on the season.
Hope that helps. With 25 days to explore Italy, you really can't go wrong. Enjoy!