January is summer holiday month in Victoria and one of the easiest times to bring children to Melbourne, with highs around 26°C and light until well after their bedtime. The average hides the swings, though. A hot northerly can push an afternoon far past comfortable before a cool change blows in from the south-west and the temperature falls within the hour, so sun hats and warm tops travel in the day bag together.
The Australian Open takes over Melbourne Park in the second half of the month, and children do not need show-court seats to enjoy it. A ground pass gets you onto the outside courts and into the AO Ballpark, a family zone for three- to twelve-year-olds with mini tennis courts and shaded seating. Under-threes go free if they are not taking a seat. The calmest days are in the qualifying week before the main draw, billed as Opening Week, when ground passes are at their cheapest and the players' practice sessions are open to watch. Once the main draw starts, pick a weekday in the first week, when the outside courts are crowded with matches, and be gone before the evening crowd arrives.
On a scorcher, head for the Ian Potter Foundation Children's Garden at the Royal Botanic Gardens, where water spouts from the ground at the Meeting Place and a little stream runs through the planting. Outside school term it opens every day, which covers most of January. The fountains stay off on days below 25°C, so keep it for the hot days and bring a change of clothes and a towel.
UV in a Melbourne summer reaches the extreme range and stays high on cool, cloudy days, which is when children burn because nobody thought to reapply. The free SunSmart app shows the day's sun protection times for where you are. Keep the playground for before and after that window, and spend the middle of the day indoors.