Florence:
My favorite area to dine in Florence is the Oltrarno district. This is the area across Ponte Vechio, and the further you go away from the bridge, the more authentic it becomes.
Closest to the bridge, is 4Leoni. They have a great bistecca but also other dishes. One of my favorites is the pear stuffed gnocchi or the peposo(kind of like a pot roast). This has made its way to several quite books though, so it is still frequented by many tourists. I would recommend reservations.

Santo Spirito is a piazza a little further in. It is great for pre-dinner cocktails. Most of the restaurants around the square included a free aperitif or aperitif buffet while you drink your wine or cocktails. It has a great vibe and is full of locals.
Casalinga is on an alley around the corner from Santo Spirito and we really enjoyed this meal. It was one of the few places where no waiter spoke english, so we had to guess a little, but the duck tortellini was amazing.

If you make it past Porto Romana, both Podere 39 and Pizzeria Antica Porto are very good also.

Keep in mind, most things close on this side of the bridge between 2-7 every day, and the restaurants that stay open are not very good. If you plan to see the Pitti Palace you can get 1/2 price admission between 8-9AM daily and again on Wednesday afternoons.

On the main side of Ponte Vecchio, the Alla Antico panini shop on Via De Neri is delicious. It is only 5Euros, huge, but, the place has a line of over 100 people by noon. If you get there a little before 11, you can avoid these lines of tour groups.

La Buchetta (close to the bridge that goes to Michaelangelos Piazza) is a great restaurant when you are craving bistecca or other cuts of meat.

Last but not least, Trattoria Sostanza has a great buttered chicken but make sure you make reservations and have Euros.

If you have an airbnb, cook at least one night. I know it is tempting to eat out every meal during your trip, but the meats from the butcher shops are sooo good. Thin cut veal, pork chops, bistecca, even their burger patties are amazing.

In Tuscany, my favorite city was Montepulciano. Pienza and San Quirico were also great, but smaller. The views from all of these cities are amazing. Since you are visiting in off season, a lot of things will be closed, but you will also feel like you have these towns all to yourself. It is a magical feeling. We also visited Orvieto (closer to room), but I felt this one could have been skipped. They are known for their underground city tours, and we skipped this, so maybe that would have made it more worthwhile. As others have said, def rent a car. Driving in Tuscany is heavenly and very easy. One of our favorite adventures, was visiting the hot springs. We went to San Filippo Hot Springs and it was great. There are piping hot waterfalls coming off of the sulphur rocks, with small pools everywhere. Since it was offseason, only 2 local families were there so it was great for exploring. There is another beautiful Hot Spring closer to Rome called Saturnia, but we did not have enough time to make the trip out there.

I don't remember a lot of the restaurants we have eaten at in Rome, except for Mimi and Cocos, down a small alley off of Piazza Navona. It was excellent.

Have a great trip.