From the train station, first-time visitors inevitably gravitate towards Piazza del Duomo and the adjacent Baptistery. Their colourful patterned exteriors make a starling contrast with the dun-toned buildings around. Each of those great buildings is remarkable inside as out, and an ascent of the Cathedral's Dome will give you astounding views over the city to the hazy Tuscan hills beyond.
After exploring the cathedral, you can escape the crowds by climbing the Campanile of Giotto, the Duomo's belltower, or visit the Museo dell'Opera del Duomo, a repository for works of art removed over the centuries from the Duomo, from the Baptistery and from the Campanile.
Next to it you can explore the Loggia del Bigallo. It contains a tiny museum relating to one of the city's oldest philanthropic institutions.
If you're in need of a break after this architectural and artistic overload, you can recharge your batteries at one of the cafés nearby Piazza della Repubblica, a square that was plannd as a showcase for the Florence Capital City at the end of the XIX century, of the newly united Italy.