Melbourne is famously unpredictable weather-wise. Locals joke about four seasons in one day, and they are not entirely wrong. Summer (December to February) brings warm days in the mid-20s to low 30s, perfect for beaches and outdoor festivals. Autumn (March to May) is arguably the best time, with stable weather and the city buzzing with the Formula 1 Grand Prix, Moomba Festival, and Melbourne Comedy Festival all packed into March.
Winter is cool and grey but brings the Melbourne International Arts Festival in October and the Royal Melbourne Show in September. The St Kilda Festival, one of Australia's biggest free music events, lights up the beachside suburb each February. There is always something on in Melbourne, so do not worry too much about timing.