@dagmaraka,
Ohhhhhhhhhhhhhhhh, yea.
Well, you can find a list of museums to lure you. I like the Bargello..
Me, if I only had a day or two not in conference, I'd walk myself silly and eat my way to happiness.
I'm mad for the buildings, and mad for piazza history.
Important to me historically is the most tourist laden piazza, but this is winter so it shouldn't be too full... pza Signoria by name, where the (many) bonfires of the vanities occurred: these were festive events at the time. The dominican monk Savonarola was a popularizer of the protests against the vanities/papacy. Not only were vanities burned but he was too, about five years later, same piazza, just about the same place in it... 1497.
In a loggia in the same piazza is Benvenuto Cellini's Perseus and the Medusa. Nice and gory for you, and also beautiful, probably my favorite sculpture.
Another square I love, probably love the best, is pza S. S. Santissima Annunziata, where I've stayed at different hotels on different trips - one, Le Due Fontane, was, at least at the time, sort of a dark rust color - we had a great room with balcony where we could look out across the piazza at sunset. At Sunset in March, there was low orange gold light cast on arcade of the church with the piazza's name. Next time I was in Firenze by myself for four days, two of them early - I lucked out at got a tiny room at the elegant Loggiato di Serviti, also on that piazza. After those two days I stayed at the also-wonderful (whatsitsname, starts with C), one street over.
What's so great about the piazza? It's beautiful and is thick with architectural history if one is interested in that. I'll make this short and sloppy - from notes.
-- first came the church, completed mid 13th century (Servite order of monks)
-- almost two centuries later, Brunelleschi's Ospedale degli Innocenti was built , following up his study of classical architecture in Rome. (I think he went there with Donatello, not sure I remember right). Brunelleschi stopped with it in 1427; an arcade with corinthian columns crosses the front of the orphanage (swaddled babies on the columns by della Robbia).
-- then part of the church was remodelled and an arcade added in harmony with the Brunelleschi work. (Michelozzo di Bartolommeo)
-- then a monastery was built (1516 - Sangallo and d'Agnolo) on the opposite side of the piazza to the orphanage, also with arcade harmonizing with Brunelleschi's, its columns having S's at the capitals instead of della Robbia bambini. (That or part of that is now the Loggiato di Serviti hotel).
If you stand in the piazza a few feet in front of the arcade of the monastery, and look to your left, you'll be looking down via dei Servi ... at Brunelleschi's duomo.
re architectural history, the positioning of the monastery predated Michelangelo's spatial arrangement of the capitoline hill buildings, another "landmark" in design planning.
Cool, but me, I just like being there.
I'll flip through my mind to see if I can think of things you might like. Back later.
Adds, in case you do decide to hit the Uffizzi, look online to see if you can get tickets. (That's new since I was there in '99)