Two things you won't forget for the rest of your life.
Visit a museum that's not crowded: Palazzo Medici Ricardi, go right up to the first floor, enter the tiny room which is the chapel of the Magi and look at the frescoes by Benozzo Gozzoli.
In the evening eat at the Cibreo (055-234-1100),best of Tuscan food with a huge list of Supertuscans (e.g. no less than 10 years of Caberlot). The chef d' will take a seat at your table to discuss your menu.
This tip has the address "cibreo, via andrea del verrocchio 8"