Itinerary for transportation Rome to Florence to Countryside and beyond

My tentative plan.
Arrive in Rome on Dec. 22. Shuttle to hotel for 3days, leaving Rome early in the morning on Xmas day, taking train to Florence.

Hang out in Florence on the 25th, then do "David" and Uffizi on the 26th and leave on the 26th in late afternoon to Siena and beyond.

I found I could pick up a rental by the train station but special holiday hours on the 26th mean rental place closes by 1pm .. guess I need to find somewhere to park the rental safely until I am through at museums. Plan is to get up early on the 26th, rent the car and park it, then back to check out of hotel and walk to museums and come back to car at end of day, drive to Siena...but? Guess I can't drive into Siena? Please help me think through this. I guess I don't need to stay in Siena that evening..I am open to suggestions.