Sure! Travelling across Australia's sprawling cities will indeed be an exciting journey. Here are some essential travel tips for you:

Best Time to Visit:
For Sydney and Melbourne, the ideal time is during spring (September - November) and autumn (March - May) when the weather is pleasant. For Gold Coast and Cairns, winter and spring, specifically from May to October, are the best times to avoid the extreme heat and the stinger season.

Route and Accessibility:
All these cities are well connected via a network of domestic flights. You can also opt for trains or self-drive between Sydney and Melbourne, and buses for local transport within the cities. In Cairns, consider renting a car for exploring the various tourist spots.

Altitude and Acclimatization:
As these cities are at sea level, acclimatization is not a concern.

Accommodation and Booking:
Accommodations range from luxury hotels to budget-friendly hostels. It is recommended to book your accommodations in advance, especially during the Australian summer (December to February), as it can get quite busy.

Clothing and Essentials:
Pack according to the season. During summer, light clothes, a hat, sunscreen, and water bottles are essentials. For winter, pack a good warm jacket. Don't forget your swimwear for beach visits and the Great Barrier Reef.

Health and Safety:
Each of these cities is quite safe for tourists. However, basic precautions like not wandering alone at night in deserted areas, keeping an eye on your belongings, and staying hydrated are recommended.

Local Etiquette and Respect:
Australians appreciate good manners. Be respectful, queue where necessary, and always clean up after yourself, especially on the beaches and public places. Also, note that restrictions may apply to alcohol consumption in public areas.