If you have an afternoon to spare while in Rome then I recommend taking a little side trip to Civita to have lunch. It's a tiny little town with beautiful views of the countryside, and you basically have the whole place to yourself. I think the name of the restaurant we ate at was Alma Civita. It was about an hour from Rome.
Civita di BagnoregioIn Rome, I would recommend wandering around the Trestevere neighborhood and just popping into a place that gets your attention. While there are some good places to eat in the city center, there are also a ton of overpriced, tourist traps. I generally try to venture out for dinner. San Lorenzo is another fun neighborhood to have dinner and drinks if you want to get out of the center. It's northeast of Termini Train Station.
It's been about 7 years since I was in Florence, and I don't remember much about where we ate.
Please return and post about your trip when your done. I'll be in Florence and Rome in December and would like to hear if you found any interesting places to eat!