2024 update: Yellow Bar is still in Florence! They have very little to no internet/social media presence, but can be found on Yelp!, TripAdvisor, etc.
Yellow Bar is a typically Tuscan restaurant and pizzeria located in the center of Florence on Via del Proconsolo. The menu offers a wide selection of Tuscan specialties, such as fresh homemade pasta and pizzas made with organic stone-ground ancient grain flour (cooked in a wood fired oven). If you have a morning visit to the Bargello or Opera del Duomo, Yellow Bar is very close and a great choice for a reasonably priced lunch with a good atmosphere and great staff. Closed Mondays!
The below is very old (originally written in 2005!) but I wouldn't say outdated - the food is still good, but the prices mentioned below have surely increased:
Our first real meal out in Florence was lunch today at the Yellow Bar (last night dinner was some bread, cheese and salami at the apartment). We had walked around for awhile and this looked like as much of a child friendly place that we came across (I noticed there was some Japanese Anime on a flat screen that the kids could watch while we ordered and waited for the food). This is probably not the most typical "Italian" restaurant you are going to find in Florence, but it was perfect for our first time with the kids in a Florentine restaurant.
My wife and I split a plate of Carbonara and a pizza Margherita, and the kids had a hamburger, a side of fries, and a bowl of pasta with butter. We had two cappuccinos after, and drank tap water. The bill was about 36€ with a 12% tip included. The best part of the meal was that everything was hot and fresh, and really delicious. We saw food go to a bunch of other tables and everything else looked good too. They have a large selection of pastas, salads, and some American style food. We will definitely be back.