Florence: Off the beaten path and most authentic Italian dinner in Florence?
Osteria Santo Spirito is one of my favourite restaurants in Florence. It is in Piazza Santo Spirito, often considered a hidden gem of the city. Definitely get the gnocchi with truffle oil and spaghetti with tomato basil...
Rome: How expensive is Rome and Florence?
Look into getting a 2 day Florence pass- about 70 euro but it will get you into all the must-see places. In Florence, you won't have to worry about transportation because you can walk everywhere. Look into Florence for Fun for day trip wine tours...