The cathedral square is filled with tourists and caricature artists during the day, strolling crowds in the early evening, and knots of students strumming guitars on the Duomo's steps at night. Though it's always crowded, the piazza's vivacity and the glittering facades of the cathedral and the baptistery doors keep it an eternal Florentine sight.
At the corner of the busy pedestrian main drag, Via Calzaiuoli, sits the pretty little Loggia del Bigallo (1351-58). Inside is a small museum of 14th-century works, which is unfortunately almost always closed. Call tel. 055-215-440 if you're interested in trying to make an appointment to get in to see the 1342 Madonna della Misericordia by the school of Bernardo Daddi, which features the earliest known cityscape view of Florence.
Note that just south of the Duomo, hidden in the tangle of medieval streets toward Piazza della Signoria, is a 14th-century Florentine house restored and converted into the Casa di Dante (tel. 055-219-416), a small museum chronicling the life and times of the great poet. But, this isn't likely the poet's actual house. The entrance is up the side alley of Via Santa Margherita, and it's open Monday and Wednesday through Saturday from 10am to 6pm (to 4pm in winter) and Sunday from 10am to 2pm. Admission has nearly tripled to a ludicrous 6.50€ ($8.45), so only die-hard fans should bother.