Tuscany is an area, not a town and to see it well you really need a car. You could go by train to Florence and take a few day trips from there to maybe Pisa and Lucca and Siena, or you could stay in the countryside in a small town, maybe Montepulciano or Pienza, and take drives around the various towns and villages, which we much prefer.
Of 13 days is your time "on the ground" then you could fit in three places, perhaps Rome 5 days, Tuscany 4 days, Sorrento 3 days then back to Rome the night before your flight, though I think you would see more by choosing Rome and Tuscany and giving each almost a week. If it includes 2 days for arriving and departing travel, then two places would be better.
Itinerary suggestion 13 days. What month are you thinking of visiting Italy ???
Rome - 3 days - Sorrento - 5 days - ( Tuscany ) - Florence - 4 days - day trip to Sienna - Rome - 1 day.
Your itinerary is not as rushed as many that we see. There's time enough to spend a few days in each place and that certainly beats the "one-night stands" in several places.
I reiterate Ellemay's thoughts on the time of year. If it's in the winter, forego the trip to Sorrento.
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