April–June and September–October are the best months: mild weather, long days, and manageable crowds. July and August are hot (30–36°C), humid, and heavily touristed. Many restaurants and shops close for two or three weeks in August when Florentines leave the city. Museum queues in peak season can be brutal without advance booking — the Uffizi and Accademia fill their timed-entry slots weeks ahead.
November through March is quieter and noticeably cheaper. The city is cold (5–12°C) and occasionally rainy, but the museums are uncrowded and the restaurants are full of locals. December has Christmas markets and fewer tourists than most Italian cities.
Estate Fiesolana (summer concerts in the Roman theatre above the city) and the Maggio Musicale Fiorentino (May–June opera and orchestral season) are worth timing a visit around for classical music.