Don't miss out on the famous local dish, bistecca fiorentina.
Rome tips; When visiting the Colosseum, first visit the Roman Forum right across from it first; you'll probably want to visit both anyway, but the lines at the Forum are WAY shorter though the combination tickets exactly the same. Saves you waiting in line for the Colosseum!
Also, if you plan on visiting the Vatican Museums (recommended); reserve online in advance. The lines at the Vatican are literally kilometres long.
Siena; Hopefully the mosaics of the cathedral are uncovered one of the days that you're there... that is one helluva thing to behold.