Central Florence is split by the Arno River. The main sights - the Duomo, the Uffizi, the Accademia - are on one side of the river, while the neighborhood known as the Oltrarno is on the other. “Oltrarno” actually means “beyond the Arno,” or “the other side of the Arno.”
Among the attractions in the Oltrarno are the massive Pitti Palace, to which the ruling Medici family moved after leaving their residence in the Palazzo Vecchio, and the sprawling Boboli Gardens behind the Pitti. You can also visit the Santo Spirito Basilica (designed by Brunelleschi, who designed the cathedral’s famous dome) and the church of Santa Maria del Carmine (with the fantastic Brancacci Chapel and its Filippino Lippi frescoes).
Keep going through the flatter part of the Oltrarno and you’ll eventually head up staircases and narrow streets into the hills overlooking the city. You know that postcard view you keep seeing all over town? You can see it for yourself from the Piazzale Michelangelo.