Thanks Tim - here's what I'm planning.
I'm landing in Genoa for a workshop and will be in Sestri Levante for a week, during which I will visit Milan for one day (and return to SL the same day). I've
already gotten a reservation for the Last Supper!
Afterwards, I'm planning to visit:
Verona, Vicenza, Padua, Castelfranco Veneto, Venice, Florence, Pisa, Sansepolcro, Rome, and Naples.
I'm flying back to the US from Rome. The whole trip will be around 3 weeks.
I've also considered what you mentioned, that a train pass is not the most cost-effective for all travels. I'm planning to purchase the Eurail Italy pass for 5 days, then purchase individually all the short-distance trains. The 5 days will mostly consists of long distance (Venice-Florence, Florence-Rome, etc), or on day trips where train use is heavy (over three cities).
For the Youth 2nd class, each day is about $30. I checked that the long distance trips is worth at least $40 each way, the heavy day trips add up to $30 (and a lot less hassle with a pass).
Does that sound like a plan?