Historically the religious heart of Florence, the Piazza del Duomo gets its name from the grand and ornate cathedral that faces it (the Basilica de Santa Maria del Fiore). The church, the fourth largest in Europe, is a wonder in itself and has served as the main religious point in Florence since its creation in the 13th century. An even greater wonder is that it even got built, since its architect, Brunoleschi, was assured by builders of the time that the building would not stand under its massive weight; Brunoleschi has apparently had the last laugh on that one. Pay the fee to climb to the viewing platform on the dome for a stellar view that is only topped by the view from the taller, adjacent bell tower, a masterpiece of Gothic architecture by Giotto.
In front of the cathedral is the Museo dell'Opera, which actually displays some excellent works of art, include those by Michelangelo, Donatello, and others (insert arbitrary Ninja Turtles reference here). The Baptistery, the Loggia del Bigallo (a gorgeous arched walkway), and a number of palazzos all call this grand piazza home, making it a place to drink in all day long as the shadows grow long and the immensity of these human accomplishments settles in.All of the religious sites on the piazza (the bell tower, baptistery, church, and museum) collectively cost 10 euros if you prepay online. Check the official website for further information.