Rise early. It won’t be hard. In this part of the world, flocks of kookaburras begin giggling at dawn, so you may not need an alarm to be roused out of bed at the brand-new Alex Hotel. The colorful rooms are filled with chic woolen blankets, quirky lighting, and other artsy touches from international designers. You’re in Northbridge, a happening neighborhood close to downtown, where you’ll find Greenhouse Perth and a classic Aussie breakfast: a flat white (espresso and steamed milk) and a soft-boiled egg with thin slices of buttered toast “soldiers” for dipping.

A short thigh-burning trek leads to the hilltop Kings Park, 1,000 acres of indigenous foliage with an aerial view of the city. Seek out the eerily majestic baobabs, a native species of tree with skeletal branches and massive trunks that have historically been used for medicine and food. From here, it’s downhill cruising. Direct your smartphone to Perth Arena, a Transformers-like stadium built in 2012 that symbolizes just how much the city has changed in recent years.

Six blocks away, check the evening schedule in the lobby of the Heath Ledger Theatre, an exceptional playhouse named after the late, Perth-raised actor. For lunch, order burgers and Sly Fox ale at the new Lot Twenty next door, or keep heading down William Street for 10 minutes to take advantage of Perth’s proximity to Southeast Asia. This part of town lays claim to a trove of Thai and Vietnamese spots that blend Oz’s fresh produce with spices that seldom cross the Pacific. Try S&T Thai for tom yum soup that will cause your tastebuds to flicker. If you’ve still got it in you, browse Post Emporium’s funky home goods on the way back to your room for a very much deserved afternoon nap.