Florence is amazing, you will love it! My top choices are Galleria Uffizi (buy tickets in advance if possible and stay as long as you wish); Ponte Vecciho (I go at night as it us beautiful - gold stores are mostly closed if that is a concern for purchasing gifts - not an issue in my mind as overpriced); Galerria Academia for David statue (less than an hour and buy tickets there if you want, people come and go quickly unlike Uffizi); and just getting lost walking through history with incredible piazzas like piazza del duomo (I go both at daytime and after dark for different look with lights on, bit either time is incredible). Enjoy!