My thoughts for you, given your timing and interests (and possible interests).
Archeology museum has an excellent and varied collection and doesn't get the crowds because there is so much other more famous stuff to see
Baptistery interior if the scaffolding has been removed from the restoring of the mosaic ceiling
Bardini Museum & Stibbert Museum if anybody likes medieval weapons and seeing interesting miscellaneous collections of ancient through Renaissance art and other stuff without the crowds of people. Also the attached Bardini gardens are smaller and less popular than the Boboli Gardens and have a great view of Florence from the top (and a cafe)
Bargello --- this is where I would go to see sculpture, maybe with a guide, maybe even instead of going to see the original David (there are two good life-size copies --- I AM an art buff and this is heresy, but I'm saying it anyway for people short on time)
Duomo Museum --- here is where you'll find the original Baptistery doors and many other wonderful things that have been removed from the Duomo for their preservation
Galileo Museum if anyone is interested in science
Medici-Riccardi Palace……the Benozzo Gozzoli chapel is, to me, worth the admission price to the whole palazzo which I skip. I don't know how busy it gets during the summer, but when I was last there before the pandemic in early October it would fill with people and then empty out over and over. It's tiny and you can see the frescoes up close --- they look like they were just painted and I think would interest even people not interested in art.
Mercato Centrale to see beautiful displays of food & there are places to eat there, too --- nice for lunch
Palazzo Davanzati to tour a medieval house rather than a huge fancy palace
Palazzo Pitti & Boboli Gardens ---skip these "classics" on this trip. I confess that I have always skipped the Pitti despite 40+ days spent in Florence --- not a fan of enormous ornate palaces. The gardens are cool but even though I am also a major gardening buff, I thought there were many better places to spend my time in Florence.
Palazzo Vecchio has old city maps if some one is a map fan and has a great view from top of tower --- we love maps, so this is on our list for next time, but I've never been there
Piazzale Michelangelo + San MIniato + the cemetery ---- you could walk up here on your very first day and get that much-needed exercise and sunlight to combat jetlag. You can instead take a taxi and then walk down the hill. You will get possibly the most classic view of Florence from the piazzale and see the exterior and interior of a small medieval Romanesque church. Also Saint Miniato was beheaded down by the river, picked up his head and walked up the steep hill to the spot where his church was later built.
Santa Croce, Santa Maria Novella, and/or Santa Trinita for seeing great art in its intended places instead of in an art gallery
Uffizi --- I don't know what to say about the Uffizi. If you want to do it, a guided tour might be good. It is huge and very crowded even first thing in the morning and overwhelming even for art buffs. The famous paintings are almost constantly blocked by people taking selfies in front of them, but there are plenty and more than plenty of excellent but less famous paintings and sculptures. I wonder if the Uffizi has evening hours in the summer that help you beat the crowds. There is a cafe for taking a break.
