It can be very difficult finding a good restaurant open between the hours of about 3pm to 7pm, as dining in those hours is alien to italian habits.
Vegetarians and vegans should have no problem eating in Florence as staff at Italian restaurants tend to be very accomodating. Try ribollita, a regional specialty vegetable soup. 100 percent vegan and delicious. Pizza in Italy (and authentic Italian restaurants elsewhere) do not use dairy products or eggs in their dough.