Hi there-
You'll probably get all sorts of suggestions but my own would be to limit it to Florence and Rome; lots to see in both!
Sunday - Tuesday (3 nights, 2.5 days) in Florence
Wed - Sat (4 nights/3.5 days) in Rome.
Fly home from Rome on Sunday.
I know the distance between Figline Vardarno (note spelling) and Florence, and Florence and Rome isn't all that far but I'll still count your transfer days as partials versus full due to the time it can take to pack up, have some breakfast, check out, make the transfer, find the new hotel and check in. If arriving too early to do that - which you probably will be - have the hotel stow your bags until you can do it later in the day. :O)
Editing to add: this itinerary will be very easy by train. I see that Firenze Santa Maria Novella (Florence's main train station) can be reached from Figline Vardarno in a little over 30 minutes or so, no changes, depending on the train you choose, and "fast trains" from SM Novella to Roma Termini (Rome's main train station) take just 90 minutes, no changes. Florence's historic center is more compact than one might think; we didn't need public transit even once during our 5 days there. Rome is a little more spread out but very walkable (and the best way to experience it, IMHO) as well unless one has some sort of mobility limitations. We've only used public transit (metro/urban train) a couple of times there over a couple of trips.