For beauty & photography, Basilica di San Miniato al Monte delivers.
A short climb above the famous terrace gets you a more beautiful view, a stunning green-and-white marble church almost to yourself, and — if you time it — monks singing Gregorian chant at dusk. The catch: it's a further uphill push that most day-trippers won't make, and the chant schedule shifts with the season so you can miss it. For the willing, it's the quietest sublime moment in Florence.