Most of the restaurants in the center of Florence, i.e. the area that is broadly defined by the Oltre arno area, Piazza Michelangelo, Santa Croce and San Lorenzo, tend to cater largely to tourists. Hence, their menu can be either very expensive or mediocre. However, it is possible to find nice places that are frequented by locals and provide enjoyable meals.
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Trattoria Baldovino - (Visited 2011)
We discovered this restaurant in the fall of 2011 and have been there several times since. Located in Via San Giuseppe, along side from the church of Santa Croce, a few meters from Piazza Santa Croce, this trattoria/restaurant offers a great, reasonable menu. Every time we visited, we were not let down and the food was very good. Baldovino is now definitely our preferred restaurant in Florence. NOTE: It has changed since the last time we were there. It is significantly more touristy, so we can't vouch about its quality.
They also have a great website where one can check the menu as well as prices.
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Trattoria Il Bargello - (Visited 2009, 2010 and 2011)
This little restaurant/trattoria is in Borgo dei Greci 37, an ideal location in the heart of Florence, between Santa Croce and Piazza della Signoria. A typical small, unpretentious trattoria frequented by florentines, with a fairly anonymous street window, a small entrance.....

We stumbled in one evening and had some of the best meal we have had in Tuscany in 2009. However, during other visits we were not as impressed, the meals were average. Not sure whether the chef moved on or we were simply either lucky the first time, or unlucky in our following visits!
In 2009, among various dishes, we had Pici al ragu'...a typical Tuscan dish. The sauce is a meat-based (tomato-less) sauce simmered for hours including celery, carrots and onions and enhanced with a "bouquet" of sage and rosemary. Definitely worth 10 euro.
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Francescovini - (Visited 2009, 2010 and 2011)
This restaurant, in Piazza de Peruzzi, just by Santa Croce, was recommended to us by Carlo from DeBenci B&B. As an appetizer, we had crostini misti followed by pappardelle al ragu and zite al pommodoro. House wine was $ 8 Euros, which is on the expensive side. Overall we spent 36.5 euros for a very decent, last minute meal. Overall we enjoyed it and would not hesitate to visit it again.
We have been in this restaurant again in 2011. It was ok, nothing exceptional, but nothing particularly bad. So, while it is not among our preferred ones, we would not hesitate to eat here whether for convenience or had no other choice nearby.
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Osteria depeccatori - NOT recommended (2009)
On September 2009, after a morning spent visiting the Bargello Museum, we were ready for lunch and stopped at the Osteria depeccatori in Piazza SanFirenze. It was clearly a place oriented for turists, but we were starving and it was late. We had a Margherita Pizza a serving of Spaghetti alla carbonara and some house wine. The cost was reasonable (5.40 Euros for the pizza, 4.90 for half a liter of house wine), in total 19.80 Euros. However, the quality was not there.
After coming home, we checked this restaurant on line. It is indeed reviewed on Trip Advisor and averages 4 stars. However, what I found of interest is that most of the poor reviews are from italian tourists, while most tourists from English-speaking country found the restaurant's food very good... with one exception. As the reviews states: "Do not eat a any restaurant that has a menu in multiple languages or has pictures! It is just a tourist trap and is in no way representative of the renowned italian cuisine that can be found elsewhere. (BrisbaneA_t)"
Salumeria/Enoteca Verdi - (Visited 2009)
If you happen to be between Santa Croce and Piazza della Signoria, in Via Verdi 37, this little salumeria-enoteca is a perfect lunch-style place, a good place to stop for lunch or an afternoon wine and cheese tasting. Though you are in the heart of historic Florence, you won't see many tourists.

They serve home cooked meals in a delicatessen style atmosphere, good hearty tuscan food, from crostini, to sun-dried tomatoes, olives, chicken, fish and sliced meats. typically, they have lots of greens such as spinach, broccoli and peppers.
You order and pick up your food at the counter, they heat it up while wait, then you take it to the tables in the back. The food is very good and the atmosphere very italian-tuscan. Try different things. When we were last there, in September 2009, we shared three types of pasta, some porchetta, etc. all at a very reasonable cost. A review of the salumeria can be found on About.com
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Dal Contedilladarno ... (Visited 2008 & 2009)

NOTE: This trattoria is now under new management and we can't speak to its quality anymore
Once upon the time....sigh... we loved this little trattoria situated in the OltreArno district of Florence. Close to Piazza di Santo Spirito and a short walk from Ponte Vecchio. It was a family run trattoria with Luca in the kitchen, and Antonio the main server, mostly frequented by locals. It was inexpensive and with very good food (it never failed us). Every time we were in Florence, we made a point of going there. The food was exceptional and in the words of a foursome sitting beside us from the US last time we were there..."This is the best food we have eaten in Italy"...not bad for a tiny, out of the way trattoria. We will try the new management, but Luca will be missed. Check out the old reviews at the following link and see what you missed: Thistle dew blog