Want delicious, authentic, intimate. Cost is irrelevant - just want memorable and fabulous.
Absolutely Trattoria Sostanza. Make sure you call ahead to book a table as the restaurant is small. We were seated right next to the kitchen and the cook was butchering the meat with tiny pieces flying in our direction. Several guests we spoke to said the steak was the best they had in their lives but we didn't try it. The chicken in butter was out of this world though. Probably the best chicken I've ever eaten and the house made dessert with wild strawberries was outstanding. A very memorable meal and we would make a point of going back the next time we are in Florence.
My favorite restaurant in Florence has to be Il Latini. It's very authentic Italian cuisine and instead of ordering off of a menu they bring you out dishes recommended by the chef. I've recommended this to a few friends who have gone to Florence and its been a hit every time. Enjoy!
It's not dinner, but when you do lunch one day of your trip, be sure to do Il Panino del Chianti at the end of the Ponte Vecchio. Order a bottle of wine and custom order your sandwich, and prepare to be amazed. It was absolutely my favorite meal in Florence!
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One more suggestion - Ristorante La Giostra. Atmosphere and food were so romantic and delicious that my husband and I went two evenings in a row, taking another couple the second night. The owner is descended from royalty, the story goes. The space used to house a merry-go-round (hence the name). There are tiny white lights everywhere and plenty of recommendations from the staff when it comes to your meal - all great. I long to go back...
I was told by a coworker to go to Il Profeta and it did NOT disappoint. The place is tiny, so I suggest going when they open because it fills up, but the owner and his wife are so nice. We told them we were told to come here by a friend in America and they kept bringing us things to try! And the food to say the least was amazing.
I strongly recommend you the restaurant Vecchio Carlino (Viale Fratelli Rosselli 17R, 50144 Firenze): the waiters are friendly and funny. Obviously, the food is delicious (try the steak: you won't regret it!). When I went there I met an American couple who has been going to Al Vecchio Carlino for 10 years, every time they come back to Florence.
Enjoy my country! :)
One of my fav restaurants is Cammillo Trattoria. It is full of locals. I love I Latini and Sostanza as well but usually you only hear English. Check out my other Best Bits at http://bestbitsworldwide.com/florence-a-25-year-love-affair/ Have fun.