Day 1: Fly into Melbourne and check into Coppersmith, a poised pub with a clever chef (and Melbourne-centric boutique bedrooms).
Day 2: Go for a rummage around the Queen Victoria Market (‘Queen Vic’ to the locals), which also has plenty of street-food stalls and pop-up bars to tempt you with.
Day 3: You’ll easily lose a day at the National Gallery of Victoria (NGV), Australia’s oldest public art museum.
Day 4–6: Once you’ve had your fill of culture, you deserve some pampering: spend time on the Mornington Peninsula (an hour from Melbourne by car) enjoying the famous Peninsula Hot Springs. Arrive by late afternoon so that you can idle in the hot pools at night, admiring the twinkling lanterns that light the way for bathers. The springs are mega popular, so be sure to book your spot in advance.
Day 7–9: Once you’re suitably relaxed, drive back to Melbourne and fly to Canberra, Australia’s capital city (flight time: 1 hour 5 minutes). Wine and dine in some of the country’s best restaurants, visit The National Gallery of Australia and tour Parliament House. If you’re in town on a Sunday shop at the Old Bus Depot markets, a hipster hangout selling great produce and homewares.
Days 10-13 Fly from Canberra to Sydney (55 minutes). Start by people-watching on Bondi and Tamarama Beach (bikinis, biceps and miniscule beach shorts a-go-go). Stay at Pier One Sydney Harbour, a nautical bolthole with harbour-view rooms and sea-fresh cuisine.
Hunt for vintage treasures at friendly Glebe Markets, held every Saturday between 10am and 4pm and if the market isn’t on, hit the boutiques in fashionable Newtown. Spend some time around the historic Rocks and climb the Sydney Harbour Bridge.