The modern nation of Australia is notorious for having been founded using British and Irish convict labor. Learn more about this cruel history at the UNESCO–listed Hyde Park Barracks, now a museum on the northern edge of the beautiful Sydney Hyde Park. The “barracks” were originally built in 1819 to house convicts; now, the exhibitions tell the stories of the convicts and the generations of people impacted by the colonial system, including First Nations peoples.

A short walk from the barracks, on the eastern side of Hyde Park, sits the stately Australian Museum, a treasure trove of artifacts that tell the stories of Australia and beyond. Like many old museums, it has revamped its traditional displays to a more contemporary format, yet it retains many of its old taxidermied animals and cases of rocks. Like many of the best museums in Sydney, entry to the permanent exhibits is free, making this a great choice for budget-conscious travelers.

You’re never far from the sea in Sydney, and you can explore stories of the country’s seafaring past and present at the Australian National Maritime Museum in Darling Harbour. The permanent (free admission) and temporary exhibits explore navigation by First Nations peoples, the First Fleet that brought British settlers to Australia, World War II history, and more. It’s a good idea to book tickets to the paid portions in advance as this museum is very popular, especially with families.

Occupying a prime spot in an art deco building in Circular Quay, with views of the Sydney Opera House, is one of Sydney’s museum highlights—the Museum of Contemporary Art Australia (MCA). MCA focuses specifically on artists who have lived and worked in Australia, and one third of its collection is work by First Nations artists, so it’s a great place to see a breadth of Australian art without traipsing around all the art galleries in Sydney.

On the edge of the Royal Botanic Garden, the Museum of Sydney is located on and around the remains of Sydney’s first government house. It’s been called one of the most significant buildings in Australia’s history, so it’s only fitting that the museum’s collections focus on the importance of Sydney in Australian history, life, and culture. If you’re traveling with kids, select a family-friendly tour that includes the Museum of Sydney alongside other attractions to keep everyone entertained.

Sydney’s Justice and Police Museum is the closest most travelers will want to get to the inside of an Australian prison. Located in an old sandstone building at Circular Quay, the museum’s collections are spread across the late-19th-century police station and holding cells, creating a truly historical atmosphere. Learn about Sydney’s criminal past and some of the colorful figures that shaped the city. Drop in during a half-day tour through the central city.

Although central Sydney is a pretty fancy place these days, it wasn’t always so. The Susannah Place Museum in the Rocks, Sydney’s oldest European neighborhood, is a row of four terraced houses that was home to some of the city’s first working-class families. They’ve been restored to look how they would have a century ago. Stop by when you’re exploring the historic precinct independently or on a guided walking tour of this storied area.

Your chance of bumping into Aussie icons such as Chris Hemsworth or Cate Blanchett in Sydney are slim-to-none—unless you visit Madame Tussauds, that is. The Sydney branch of the popular global waxworks museum chain is great fun for both adults and kids, and it’s conveniently located at Aquarium Wharf at Darling Harbour. Don’t worry if you’re not familiar with many Australian celebs: International stars—from Harry Styles to Beyoncé—also make an appearance.

While exploring Sydney’s cultural institutions, don’t overlook Vaucluse House, in the eastern neighborhood of Vaucluse. This 19th-century manor has an interesting story: It started life as a humble cottage built for an Irish knight, Sir Henry Browne Hayes, who was transported to Australia for kidnapping an heiress. It was subsequently owned by influential New South Wales statesman William Wentworth, and the house and grounds grew over the decades, in 1915 it was turned into a historical museum.