Sam, when visiting Florence, try to have lunch or dinner at the terrace at San Michele in Fiesole high above Florence.
The service, food and wine are all excellent, and the views are tremendous.
If you are able to travel outside the city (about 20 clicks), here's a wonderful rustic restaurant with wonderful views; recco from the Times and my wine diary:
NYTimes letter: Da Delfina, via della Chiesa, Artimino Carmignano Tuscany. 12 miles north of Florence. Spectacular view of hills and faces a beautiful Medici villas built by Buontalenti as a hunting lodge. Simple but refined Tuscan food, about $75 for two with good wine. Charming people.
Lovely restaurant, superb view, charming people.
In Rome, I take pot luck -- there are so many good restaurants and they change so often, asking at your hotel works extremely well. Tougher in Florence which is much more touristic; Rome is much more like New York City with a more vibrant food and wine scene.
Have fun. Regards, Bob