Catch the Fireworks
Australia Day (Jan 26) commemorates the arrival of the First Fleet in Australia. The main celebrations in Perth are around Perth Water, climaxing with a massive fireworks display set off from moored barges. It's free and draws over 300,000 people, so you need to stake out a vantage point early or, if you're staying in a hotel with river views, make sure you're at the window!
Find Me a Swan
The black swan is the state emblem, and the Swan River was named after it, but sadly has very few, because most of the swans' preferred habitat, the shallows, has been destroyed. Lake Monger, 3.5km (2 miles) northwest of the city, usually has hundreds by its shores, plus cormorants, native ducks, herons, coots, and swamp hens. Taxi is the easiest way to get here; ask for Lake Monger Drive.