We want a relaxing vibe and are big foodies.
The Emilia-Romagna region is considered by many to be the food capital of Italy (although every region is proud of it's local specialties). Think Parma ham, Parmigiano-Reggiano cheese, etc. Bologna isn't covered in the RS guidebook but plenty of others do.
And since you mentioned "relaxing vibe" but not an interest in ancient/medieval history or museums than you might want to rethink staying a few nites in Rome. Great city but I don't think may people would call it relaxing although it does have some great restaurants.
As for Sorrento, it depends on what you are looking for. Good food and places like Pompeii to visit, but Sorrento doesn't have a beach to relax on. You'd need to go to a nearby town. It's about 3 hours by train from Florence to Naples, figure another 1.5 hours to get to Sorrento. With a similar amount of travel time you could instead visit a town in the lovely Cinque Terre region but avoid the actual five towns except perhaps as a day trip. The RS Village Italy tour stays in Levanto these days and it's a smaller but enjoyable town. Or south a few miles from the CT is Lerici, written up in the NYT which in 2010 said "Lerici holds much of the same appeal as its more popular neighbors, with beautiful swaths of beach and miles of hiking trails with photogenic vistas, minus the suffocating crowds." You'd probably need a car to get to Lerici and for a first trip it depends on how adventurous you are since in many shops English is not spoken. And Santa Margherita Ligure north of the CT is another charming town you can find discussed here on the forum.