Well...somewhere in a shoebox I have a small stash of business cards from Florence and also our travels throughout Chianti, but cannot find it right now under the piles of legos and other post Christmas detritus. Here's what I found based on my memory:
Cibreo. World class and old school, like Taillevent or La Tour D'Argent. Absolutely worth it if you want the over the top, multiple course, once in a lifetime experience. Favio Picchi is kind of renowned for being a bit of a nut, and when we went, he was on a very traditional almost Renaissance-era Medici inspired menu, but it was great. What's also awesome is that he operates a trattoria right next door to the main restaurant, that serves a significant portion of the restaurant menu a la carte, and without the fancy service. So you can experience the food for a lot less money and investment of time. The one place I would not miss. http://www.edizioniteatrodelsalecibreof ... 2&Itemid=2
The following three places are pretty traditional, straightforward Trattoria/Osteria, but we had very good meals at all three. Scroll through the galleries on their sites and you'll get the idea.http://www.ilcantinonedifirenze.it/http://www.illatini.com/?lang=enhttp://www.trattorialemossacce.it/
A couple of wine bars I highly recommend:
Le Volpe L'Uva is right near the entrance to the Medici Gardens at the Piti Palace, so you'll likely be near there anyway. It would be an ideal lunch spot. Their selection of wines will basically be almost entirely stuff you are unlikely to see here (and all awesome), paired with very simple wine-friendly food (cheese and charcuterie plates).http://www.levolpieluva.com/Le_volpi/Prima_en.html
Les Barriques is a larger enoteca with attached restaurant, south of the river, in an area more frequented by locals than tourists. Worth it for the excuse to explore a little further afield, but walkable from the area around the Duomo, where you will likely stay as that is where most of the hotels are located.http://www.enotecalebarrique.com/php/index.php?lang=en
The Cantineta Antinori is not inexpensive, but it is near the shopping/high fashion district, so you may find yourself nearby. The food there is very good, and best of all they glass pour most of their wines, including the high end Super Tuscans like Solaia and Tignanello which would only set you back something like $100 a bottle or more over here, so you can try these amazing wines without investing in the whole bottle.http://www.cantinetta-antinori.com/sezi ... p?IdSez1=1
The Mercato Centrale is super near the Duomo and is a really fun food experience. I would highly recommend stocking up there before leaving the city, the nearest thing to our agriturismo was basically the Italian equivalent of a Kroger - which is nothing to complain about - but had we known we would have gotten some really cool stuff at the mercato and then hauled it out with us. On the smaller outlying towns, there are still markets, but they are only on specific days of the week, so if you do not plan ahead, it will be the Italian Kroger for you.
Outside of Florence I don't have any specific recommendations. In Castellina we found a great restaurant on the main piazza, and an equally great wine shop with a tasting bar nearby. But that was just us driving into town and finding what was open, which in some of the Chianti towns isn't much. Maybe it was the romanticism of the whole trip, but I don't recall having a bad meal or glass of wine, and I am a total snob. Lucca is a little bigger, doing some research ahead of time would probably be a good idea (Lonely Planet and Frommer's have never steered me wrong), especially if you walk the walls of the old city, which is beautiful and worth it, but could take up a chunk of your trip there.