The Centro Storico is the dense medieval and Renaissance heart of Florence — a UNESCO World Heritage core small enough to cross on foot in twenty minutes, yet holding a concentration of art and architecture matched almost nowhere else. It runs from the Duomo and the Baptistery down through the narrow streets to Piazza della Signoria, the Uffizi, and the Arno at the Ponte Vecchio.
This is where Florence shows off: Brunelleschi's dome and Giotto's campanile over the cathedral square; the open-air sculpture museum of the Loggia dei Lanzi beside the Palazzo Vecchio; the Bargello's Donatellos and Michelangelos; Orsanmichele's guild statues. The streets between are lined with leather shops, historic cafés, and gelaterie, and the crowds are constant — early morning and evening are the calmest times to walk it.
It is the obvious base for a first visit. Almost every must-see is within these few blocks, so plan to book the Uffizi and the cathedral complex ahead, then let the rest unfold on foot.