April through June and September to mid-October are the easiest months. The weather is warm but not blistering, the cruise-ship day-trippers from Livorno are still tolerable, and you can climb the tower without queuing in the sun.
July and August are hot, with daytime highs of 32–35°C and crowds that make the Campo dei Miracoli unpleasant from mid-morning to evening. Book the tower for first or last slot of the day. Many restaurants close for two weeks in mid-August.
Winter is quiet and damp, with daytime highs of 8–12°C and occasional Tuscan fog over the river. The Campo dei Miracoli is at its most photogenic in February with empty lawns and low light. The big local festival is the Luminara di San Ranieri on 16 June, when the riverbanks are lined with 70,000 candles in glass jars — book a room months ahead.