Where can you go visa-free with an Australian Travel Document?

For Australian Convention Travel Document (refugees or non-Australian citizens)

According to this Wikipedia entry an Australia CTD holder is allowed into:

Asia

• Macau - Visa on arrival 30 days maximum, visa issued upon arrival for MOP100

Europe

• Germany - Visa not required 90 days (require CTD valid for at least 4 months)
• Hungary - Visa not required 90 days
• Slovakia - Visa not required
• Slovenia - Visa not required

Oceania

• New Zealand - Freedom of movement - For holders of Australian permanent visas only (according to Trans-Tasman Travel Arrangement)

For Australian citizens and passport holders (2019)

According to this website an Australian passport holder has visa free conditions in:

East Asia

• Hong Kong - 90 days
• Japan - 90 days
• South Korea - 90 days
• Taiwan - 90 days

Central Asia

• Kazakhstan - 30 days
• Kyrgyzstan - 60 days

Southeast Asia

• Indonesia - 30 days
• Malaysia - 90 days
• Philippines - 30 days
• Singapore - 90 days
• Thailand - 30 days; maximum of 2 visit a year if not arriving by air
• Vietnam - 30 days if only staying in Phu Quoc

Middle East / West Asia

• Armenia - 180 days
• Cyprus - 90 days in every 180 days
• Georgia - 365 days
• Israel - 90 days
• Palestine
• Qatar - 30 days

East Africa

• Mauritius - 90 days
• Reunion - 90 days (French territory)
• Mayotte - 90 days (French territory)

North Africa

• Morocco - 90 days
• Tunisia - 90 days

South Africa

• Botswana - 90 days per year
• Gambia - 90 days
• Lesotho - 14 days
• Namibia - 90 days
• South Africa - 90 days
• Eswatini (Swaziland) - 30 days

West Africa

• Gambia - 90 days

North America

• Canada - 180 days
• Greenland - applies as Schengen visa; 90 days in 180 days
• Mexico - 180 days - get a tourist card
• United States of America - must get an ESTA; valid for two years

Central America

• Aruba - 90 days; can be extended up to 180 days
• Antigua and Barbuda - 30 days
• Bahamas - 90 days
• Barbados - 180 days
• Belize - 30 days
• Bermuda - 180 days; will be determined upon arrival
• Cayman Islands - 180 days
• Costa Rica - 90 days
• Curacao - 90 days
• Dominica - 180 days
• Dominican Republic - 90 days
• El Salvador - 90 days
• Guatemala - 90 days
• Grenada - 90 days
• Haiti - 90 days
• Honduras - 90 days
• Jamaica - 180 days
• Nicaragua - 90 days
• Saint Kitts and Nevis - 90 days
• Saint Lucia - 6 weeks
• Turks and Caicos - 90 days
• Panama - 180 days

South America

• Argentina - 90 days
• Brazil - 90 days starting June 17, 2019 - More tips on things to know before arriving - in Brazil
• Bolivia - 90 days
• Chile -90 days; must pay reciprocity fee of $117
• Colombia - 90 days; can be extended for another 90 days per calendar year - must show an exit ticket and Yellow Fever vaccination if coming from Brazil, Uganda, and Dominican Republic
• Ecuador - 90 days
• Guyana - 90 days
• Peru - 183 days - must show a return ticket
• Venezuela - 90 days
• Uruguay - 90 days

Schengen Area States

Australian passport holders and citizens can enter, stay, and travel in these countries for 90 days in a 180-day period. You can move freely and cross the border without having to cross a border security or passport checkpoint. Remember that it is 90 days for the entire Schengen area not per country.

• Austria
• France
• Latvia
• Norway
• Spain
• Belgium
• Germany
• Liechtenstein
• Poland
• Switzerland
• Czech Republic
• Greece
• Lithuania
• Portugal
• Denmark
• Hungary
• Luxembourg
• Slovakia
• Estonia
• Iceland
• Malta
• Slovenia
• Finland
• Italy
• Netherlands
• Sweden

Non-Schengen Countries

• Albania - 90 days
• Andorra
• Belarus - 30 days must arrive visa Minsk Airport
• Bulgaria - 90 days within the 180-day period
• Croatia - 90 days within the 180-day period
• Ireland - 90 days, must show the purpose of travel, sufficient fund, return ticket, and accommodation booking
• Kosovo - 90 days
• Macedonia - 90 days
• Moldova - 90 days
• Monaco - 90 days within the 180-day
• Montenegro - 90 days
• Romania - 90 days within the 180-day
• San Marino
• Serbia - 90 days
• Ukraine - 90 days within 180-day
• United Kingdom - 180 days must show return ticket and accommodation booking
• Vatican City

Oceania

• Fiji - 120 days
• Kiribati - 120 days
• Micronesia - 30 days
• New Zealand - freedom of movement
• Palau - 180 days
• Vanuatu - 30 days

You can also check this website and this newspaper article to verify visa requirements for Australian citizens...