Florence keeps most of what people cross the world to see on the flat north bank of the Arno, from the Duomo to the queue for the David. In April the better half of the city is across the river, on the Oltrarno hillside, where the gardens come into flower one after another, and they are the reason to come.
Easter Sunday brings the Scoppio del Carro. In the morning a towering painted cart, the Brindellone, is drawn by white oxen into the square between the Baptistery and the Duomo, and during Mass a dove-shaped rocket, the Colombina, runs along a wire from the high altar, out through the cathedral doors and into the cart, which duly explodes. The city traces the custom back to the First Crusade and performs it with the straight face that very old customs are owed. Easter wanders between late March and late April, and the crowd wanders with it, so check the date before you choose your week.
Boboli, the Medici hillside behind the Pitti Palace, is the grand garden, all statues and fountains, and Buontalenti's grotto is the most extravagant thing in it. The Bardini, a short climb away, is smaller and, on balance, better. Its wisteria pergola, some seventy metres long, flowers some time between mid-April and early May and holds its best colour for about ten days, with the whole of Florence laid out beyond it.
The Iris Garden, on the slope below Piazzale Michelangelo, opens for its short season on 25 April and normally closes around 20 May. Entry is free. The iris has been the city's emblem for centuries, so a few weeks in the sun seem only fair. Its opening day is Liberation Day, a national holiday, and when that makes a long weekend the Oltrarno fills up again.
The Bardini keeps a webcam trained on the pergola. Look at it before you set out: ten days is a short window, and the climb is steep enough that you will want to know the flowers are out.