Eli Orzessek tries out some of the best cultural offerings Sydney has to offer.

There's never a shortage of things to do in Sydney, particularly if you're a patron of the arts. If you're heading across the ditch – or you're already there – these are the shows and exhibitions you can't miss while you're visiting. And with hot summer days on the menu, you can't go wrong with a bit of inside-time, complete with air conditioning.

Mammoths: Giants of the Ice Age

Australian Museum

Meet a 42,000-year-old preserved baby mammoth in this fascinating exhibit at the Australian Museum. Named Lyuba (meaning "love" in Russian), she's travelled a long way since being found in frozen mud in Siberia. Originally discovered by a reindeer herder, the baby mammoth had disappeared when he returned with a team of scientists to recover her. She was later found propped up against the door of a shop in a nearby village, where a dog had chewed off her tail and one of her ears. Despite her rough beginnings, Lyuba is remarkably well-preserved, with her skin and internal organs intact – there was even milk found in her belly. Kids and adults alike will enjoy getting up close to this rather cute specimen.


Also of interest is the beautifully curated 200 Treasures in the Westpac Long Gallery. Newly restored, the gallery showcases 100 people and 100 objects, revealing their sometimes unexpected stories. You'll find everything from an Egyptian mummy and tomb to Australia's first bank note and the feathered cape Captain Cook was given on his last fatal visit to Hawaii in 1778.

Mammoths: Giants of the Ice Age runs until May 13.

Muriel's Wedding the Musical

Roslyn Packer Theatre

Muriel Heslop moves from screen to stage in this fantastic adaptation of the iconic Aussie film – and it really doesn't get any more Australian than this. Showing at the Roslyn Packer Theatre in The Rocks, Muriel's Wedding the Musical brings the story from the 90s to the present day, complete with social media – making it at times like The Unbreakable Kimmy Schmidt set in Sydney. Somehow, it really works – and Maggie McKenna shines in the lead role.

There's even special appearances from the members of ABBA, who really steal the show when they appear as Muriel's guardian angels. But the other star is Sydney itself – the show plays great tribute to the city and the misfits who have made it their home.

Muriel's Wedding: The Musical run until January 27.

Pippilotti Rist: Sip My Ocean

Museum of Contemporary Art

This retrospective at Sydney's Museum of Contemporary Art (MCA) is a calming oasis in the heat and hustle of the city. Curated by Natasha Bullock, the show explores the Swiss artist's themes of colour, nature, the body and technology. If you've never heard of Pippilotti Rist, you've probably seen her referenced – Beyonce's celebrated Hold Up video is a homage to her film work Ever is Over all, which sees Rist gleefully smashing car windows with an oversized flower.

A highlight of the show that will be much appreciated by anyone who's been walking around Sydney all day is 4th Floor to Mildness from the Mildness Family – an installation consisting of a room full of beds, just asking for you to lie on them. Gaze up at the ceiling and lily pad shaped projections of water, plants and abstract bodies swirl above you, as if you're floating just under the surface of a pond.

There's so much to look at in this show – you could easily whittle away a good portion of the day sitting on the oversized Alice in Wonderland-esque furniture and watching Rist's entire oeuvre. Once you're done, go for lunch at Graze restaurant at the gallery – the brussel sprouts are delicious.

Pippilotti Rist: Sip My Ocean runs until February 18.

Beautiful: The Carole King Musical

Lyric Theatre

For a blast from the past and lots of familiar melodies, Beautiful has got it going on. Currently showing at the Star's Lyric Theatre, this musical follows the life and work of singer-songwriter Carole King, with Esther Hannaford in the title role. Starting with a 16-year-old King selling her first song at the Brill Building, Beautiful explores her tumultuous relationship with lyricist Gerry Goffin, with spirited performances of their well-known hits – think Will You Still Love Me Tomorrow, Unchained Melody and The Locomotion. Their eventual breakup leads to the peak of the show, Carole King's performance of her Tapestry album at Carnegie Hall in 1971

Beautiful: The Carole King Musical runs until February 4.

Rembrandt and the Dutch Golden Age

Art Gallery of New South Wales

Immerse yourself in the works of the 17th Century Dutch masters at the Art Gallery of New South Wales, where treasures from the renowned Rijksmuseum are currently on display. The exhibition's spaces have been designed by Sydney architect Richard Johnson, with Rembrandt's works housed in a bay built to the same proportions as the Gallery of Honour in the Rijksmuseum, Amsterdam. As well as other works by his contemporaries, there's a chance to see a rare work by Vermeer – Woman Reading a Letter – which drew crowds while I was there.

If you're visiting the gift shop, treat yourself to a block of 17th Century style chocolate – it's truly divine.

As part of the Sydney Festival, the Australian Bradenburg Orchestra is presenting a Rembrandt Live event to pair with the exhibition. For more from the Sydney Festival, check out Herald arts editor Dionne Christian's round up of the best on offer.

Rembrandt and the Dutch Golden Age runs until February 18.