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It looks like you will have 7 NIGHTS from arrival til flight from Florence to Brindisi. You want to see some of Rome and Florence and the Tuscan countryside.
7 NIGHTS gives you 6 days of sightseeing.
Florence deserves 3 nights, Rome needs 3 bare minimum and since your arrival/jet lag day is Rome I’d give Rome that 4th night.
For the Tuscan hill towns you really need a car and more than a day. You can do a day trip from Florence and see a bit.
2 options
Arrive Rome- what time?
Rome 4 nights gives you 3 full days
Train to Florence
Florence 3 nights w/day trip to Siena (or not)
Or
Arrive Rome
Rome 3 nights gives you 2 full days
Train to Florence
Florence 4 nights with 1, possibly 2 day trips
Make your list of must dos in each city- then decide
You are not there over a Monday so don't need to worry abut closures! (well your arrival am is a Mon but you don't want to be indoors that day)