The Mille Miglia is coming through Florence, I think today (Saturday) - and is scheduled to come straight through the heart of town. Of course the Italian websites are confusing and incomplete, and every other one has different dates and times... but I did see plastic barriers in the Piazza Signoria this morning and overheard someone at a bar talking about the race. It seems the first of the cars are scheduled to arrive in town sometime after 2:00 PM.
Here is a video from the start of this year's race I think: