May, June and September are the best months. The weather is warm enough to swim — the sea hits 20°C from June onwards and stays there until October — but the crowds and prices are nowhere near peak. July and August are hot, busy and expensive; if you do come then, book everything well in advance and expect traffic.
Late July is Jazz à Juan, the long-running festival in the pine grove at Juan-les-Pins — worth timing a visit around if you like jazz. April and October are quieter and good for walking the cap; some of the museums close on Mondays year-round.
Winters are mild — daytime highs around 12-15°C — and the old town is genuinely pleasant out of season, with most restaurants and the market open and few visitors. The downside is that many of the cap-d'Antibes hotels and beach clubs close from November to Easter.