@ossobuco,
I rememberred the other place I like with a view.
If you are up on the Campidoglio (designed by Michelangelo) walk behind the Senate building - you can look over a wall and see the forum stretch out below.
On Florence -
Like the books by Mary McCarthy - Stones of Florence, and Venice Observed.
On Venice, before I forget, like James Morris' Venice.
Back to Florence -
* Favorite gallery, the Uffizi; favorite paintings there, Duccio's Rucellai Madonna, and Uccello's Battle of San Romano
* I also liked the Bargello museo
* probably favorite painting in spot it was painted in - the Fra Angelico at the head of the stairs in the Monastery of San Marco
* favorite sculpture - Cellini's Perseus with the head of Medusa, in the Loggia dei Lanzi in Piazza Signoria.
* favorite piazza, especially around sunset, pz. Santa Santissima Annunziata
* favorite church, maybe Sta. Maria del Carmine
* favorite gardens - the Medici Villas in the suburb Sesto Fiorentino - Villa Castello and Villa Petraia. Wish I'd seen the one I really wanted to see - for the design - Villa Gamberaia, near Settignano. It used to be that you had to make an appointment, which is why I didn't get there, but I think it is open to the public more now (I'm not positive).
Last time I was in Florence (4 days) I mostly walked and walked and ate when I was hungry - and I don't remember much about the places I ate. One on the Alt Arno side of the river, just picked it for the good sounding food on the chalkboard outside. Another day I ate at a touristy looking place, Ristorante Sasso di Dante, somewhere by the Duomo, when it was starting to pour rain. Turned out not to be crowded and I talked with the waitress about piazzas, and she listed for me some of her favorites, thus much of my walking. And.. the ribollito was good.
There's a well thought of (or was) ristorante called Il Cibreo that has a less expensive cafe that I wanted to try; I never did get there. Same with a place I walked by at the wrong time to go in, on Via Tornibuoni. Looked good.. I seem to remember it had something to do with the Antinori family.
Just looked it up and there's a Cantinetta Antinori on piazza Antinori - I'd have to look at a map to see if that's the same place. Or maybe I'm just wrong about it being on Tornibuoni.
Here's a link -
http://www.10best.com/Florence,Italy/Restaurants/Lunch/22588/Cantinetta_Antinori_Florence_IT/
I went crazy and bought a bunch of ceramic dishes at a cookware type store on Via dei Servi (goes between the Duomo and pza SS Annunziata) - they mailed them home for me and all that wasn't terribly expensive, then. They were not the best possible ceramics, but I loved the colors and the heft of them, still love them. (I did get a really good plate in Faenza, home of a lot of ceramic workshops), but that's not near Florence. Also bought some nifty costume jewelry at a little tiny shop on that street. May or may not still be there. There's also an inviting pasticceria towards the SS Annuziata end of via dei Servi. Bought a leather purse at some shop somewhere.. on the Dome side of the Arno - that was fun - and I still have it. (I hardly spent any money on that last trip, Ms. Thrift, but had a wild day there in Florence and another one in Faenza.)
Um, I liked Michelangelo's library that's connected with San Lorenzo church, I think (it's been a while).
Side trips - I love both Siena and Lucca, and am fond of Arezzo too - of them, I'd pick Siena. But, for me that's really another trip re timing. 12 days fly by and you're visiting places that are dense with interesting things to see already.
Or, again, maybe not. Siena's another city I like to walk, a city I'm fascinated by the history of, and I love the countryside all around there (don't get her started). But, the first time I was there, my husband and I just went to Siena to cash a traveller's check (long story), had a cappuccino and left again. Not only did I have to go back one day, but have been back twice. Talk about art.. art that makes me weep. On ceramics, there are inviting ceramics on the walls in a lot of the shops..