I second the suggestion to get tickets on line for the Uffizi and the Accademia. When you walk up to the door and go right in at your appointed time, you will feel sorry for those stuck in the enormously long line ouside. We have used this website to get tickets in many Italian cities and have never been disappointed.
https://selectitaly.com/
It has been 7 years since our trip to Florence, but my travel journal says that I enjoyed the following restaurants (and I checked that they are still there):
Cippolla Rosa -- Next to the Medici Chapel - we enjoyed it so much the first time, we went back again later in the week.
https://www.osteriacipollarossa.com/
The Golden View Open Bar -- on the South Bank of the Arno River, across from the Uffizi - the food was great and the view was indeed golden from our waterfront table.
Home - Golden View Open Bar Firenze
Here are some suggestions for slightly "off the beaten track" things to do
1. Go to the opera at St. Mark's English Church. It is a very intimate venue and we enjoyed a lovely performance of
Carmen there. The proceeds go to help orphaned children in Africa.
Opera at St Mark's Church Florence, a unique intimate venue
2. Stop in the small, simple Church of Santa Margherita dei Cerchi, in which you will find the crypt of Dante's great love, Beatrice Portinari. The lovelorn leave notes and letters for Beatrice in the two wicker baskets that sit next to her burial vault. If you are bold enough, you can pull some out to read. Written in all all hands and every language, they pour out their hopes and dreams to a young woman who died over 700 years ago. The most poignant one I read said simply (in English), "I just want to find someone to love me."
3. If you are in shape to climb 463 steps, you can go up to the the top of the Duomo. Climbing through the rabbit warren of tunnels between the inner and outer domes, you can appreciate the genius of Brunelleschi the architect. Twice on the way up, the stairs stop and you are on one of the two inner balconies that circle the great dome at its base. The congregants below look like ants and you have a spectacular view of Vasari's painting that covers the inner surface of the dome. The real reward, however, is the view outside, from the top of the dome. You get a 360 degree view out over Florence and the surrounding countryside.
4. Walk out of town, south of the Arno, to the hill known as Bellosguardo. Within half a mile of the Arno, the city stops and you will be surrounded by stone walls, olive groves and old farmhouses. When you finally get to the top of the hill, you can look back at the picture postcard view of the city, with Brunelleschi's great red tiled dome rising there in the middle of it.
5. Go to the flea market in the Giardino della Fortezza. Lots of interesting stuff and interesting people to watch. It is held on the third weekend of every month.
Edit to Add: If you do go to the Uffizi, which is very large, I recommend buying a detailed gallery guide ahead of time. That way, you can focus on what you really want to see. It also allows you to avoid the scrum that forms around the explanatory placards. Both will make your visit much more time efficient. We have done this for many of the world famous museums we have visited. This is the guide we took with us.
https://www.amazon.com/Uffizi-Offic...1&sr=8-1-spell&keywords=Uffizzi+gallery+guide