As a Sumatran tiger leaps up and hovers over my head, I let out a shriek and think “that’s it, I’m dead meat”. The kingsize kitty is no more than a metre away and by the looks of its big hungry eyes and watering kisser, it’s ready to rumble. If I was to try to fend it off, where would I begin?

I try to recall what ruse Mick Dundee from Crocodile Dundee used to put wild animals under his spell. A simple curl of the wrist, flick of the fingers and peeled beady eyes, is the picture I conjure and consider. Otherwise, make a run for it. Or, I could stop being such a chicken-hearted sissy and give the creature what it wants, without making such a fuss.

As much as I’d like to (and for you to) think I’m brazenly trekking through pockets of the Indonesian jungle, I’m actually at Canberra’s National Zoo. A fence divides myself from the tiger which has has no (obvious) desire to turn me into dead meat; it simply wants the chunks of it that are dangling from tongs in my shaking hands.

His name is Berani which, in Indonesian, stands for “brave”. Determined not to be branded the Indonesian equivalent of the opposite, my third attempt is a success as I clink the tongs between the wire fence and the big orange cat manages to gobble my offering – this time before I take a startled jump back.

I’m on a ZooVenture tour, one the most hands-on animal adventure tours in the world (costs $95 on weekdays and $125 on weekends) which offers rare and close-up animal experiences.

“No kidding”, I think as, at the next stop, we’re throwing fish bait at a collection of oriental small-clawed otters from a perch so close, I might as well be flapping around in the drink with them.

Next up (literally) are the giraffes: Humbekhal, aka “Hummer”, and Ketanga, Hummer’s little bro. These guys stand so tall, we feed them some vegetables from an elevated walkway.

Next, it’s time to hang out with the grizzlies. The European brown bears – named Blondie, Dark Girl and Brutus – don’t scare me too much. They actually look quite cuddly. That is, until I’m asked to paint my palm with a mix of Weeties and honey and let one of them lick it off. Not only does this err on the side of icky, I’m wondering if they’re capable of having a little nibble on more than what’s spread on my hands.

“They’re actually very gentle, it will feel a bit tingly more than anything,” the guide said.

An interesting sensation, but once is enough of those sticky shenanigans, I decided.

Lego land

As strange a comparison as it is, this zoo actually sums up my overall impression of Canberra quite nicely: a mixture of educational adventure and excited buzz, with a sprinkling of foreboding qualms.

Driving around the city to begin with (to get the agitation out of the way), has a certain element of “What the?” Lego-like avenues and higgledy-piggledy roundabouts make navigating around a rather arduous enterprise at times, although it can be so ridiculous, it’s funny (for the passenger). Expect to get lost a few times anyway.

As far as the city’s design goes, it was heavily influenced by the “garden city” movement, meaning that it has loads of areas bursting with natural vegetation. So much so, that the city has earnt the title “bush capital”.

“At least it’s got something going for it,” some cynics that consider Canberra to be the out-of-date meat in a state sandwich that rates Melbourne and Sydney more appetising, might say.

But this city, I discovered, has more exquisite layers than people realise. If you’re going for a holiday or passing through, make sure to check out these must-see attractions (along with King O’Malley’s: great food and atmosphere; and a walk around Lake Burley Griffin).

Parliament house

Canberra’s political spikes turn off some people, but a visit to the home of Australia’s Parliament is a must, especially because it is the focal point of the city. The building – opened by her Majesty Queen Elizabeth II on 1988 – offers a journey through the country’s history via a collection of art and architectural showpieces, filled with marble and timber and impressively dotted with mosaics and paintings. Make sure to check out Tom Robert’s painting and Red Ochre Cove, by local artist Mandy Martin, before making your way up to the roof for the spectacular view. Also, see if you can sit in on a Parliamentary meeting or Question Time while you’re there, or go on a free guided tour.

Australian War Memorial

Having travelled extensively around the world (and hence visited many museums), it’s a great complement to list the Australian War Museum as one of my favourites. It commemorates the 102,000 Australians who lost their lives to war and is well worth spending a few hours sifting through. The latest exhibition space in ANZAC Hall offers the chance to see three different sound-and-light shows. I recommend Striking by Night; it recreates a night-bombing operation over Germany and provides a chilling insight. You can also score a free guided tour here.

The Old Bus Depot

If you’re in Canberra on a Sunday, this is the place to go (21 Wentworth Avenue, Kingston). The Old Bus Depot markets – including more than 200 stalls – are an institution in the city, having run for more than 10 years. You’ll be able to treat yourself or someone else with their massive range of handcrafted items (jewellery, toys, textiles, designer knitwear, Japanese lanterns, handpainted scarves and wraps), plus feast on a lot of fresh produce straight from the farm.

Cockington Green Gardens

The Cockington Green Gardens are something special. Family-owned and operated, they feature a display of miniature buildings from around the globe (particularly England) set in colourful landscaped gardens. Twenty countries are currently represented, so if you can’t afford the around-the-world ticket, have a compensatory look around here. It’s also a lovely place to enjoy a picnic or barbecue with plenty of facilities available.

Australian Institute of Sport

If you’re anything like me, there was a time in your childhood when you wanted to be an elite athlete. The AIS shows you what it would have been like to be that person. You’ll be able to see where the athletes train before big competitions and live the dream, via an interactive sports exhibit. Football fans will enjoy the “penalty shoot out”, but be sure to take some time to see the memorabilia on display from sporting legends, such as Sir Donald Bradman and Rod Laver. Game, set, and match.