The Singapore River swings like a lazy S through this island-city-country just a fish-ball throw from the southern tip of Malaysia. Yet Singapore lacks the grime and chaos of much of south-east Asia. Parts of it are cartoon-clean. It's not Sesame Street, but close.

As we pass through Customs at the airport some of my fellow passengers veer through the Red Lane to declare the cigarettes they have brought with them into the country and to pay GST on them – yes, really! Welcome to Singapore.

We behave well because Singapore Airport has the largest closed-circuit TV (CCTV) system in the world with 3,000 cameras trained on us all. You can bet no one is chewing gum, either. It's illegal, like many other things here.

The whole place seems so sanitised and squeaky clean – and G-rated – that I am surprised there is not a big sign somewhere: "This country is brought to you by the Letter S."

9am Socks Slurp

Roll out of bed with a coffee-urge. Only place to go is to Ya Kun Kaya Toast. There are several in town, but we choose the one at Far East Square near Chinatown. This shady nook is simple – chunky stools and tables and a brief menu – at this time of day, anyway. Kaya (coconut jam) is smothered on thick slabs of charcoal-grilled toast and paired with "coffee in a sock". Not as bad as it sounds. The sock is clean. Actually it's not a sock at all, but a knitted bag they drip-filter the local-style kopi through. It's strong, thick and, best of all, therapeutic (don't ask!).

9.30am Strange Sanctions

A local friend joins me and fast-talks the rules of this town. They used to joke Singapore was a "fine place to visit". I even have a T-shirt that says that. It's because some time back almost anything that seemed fun was declared illegal– with hefty fines attached. There are weird laws too. Toilets must be flushed, there's no littering or spitting in the street, and while bubble gum is out, Nicorette has been allowed back in. Long hair used to be forbidden, but there is still zero tolerance for drugs. The death penalty for carrying or using drugs stands, and you'd be crazy to ignore this. I already knew that.

10.15am Shopping

The fun thing about Singapore is that you can switch cultures within a couple of kilometres. Now we are off to India – well, Little India anyway – using the super-fast and efficient MRT (Mass Rapid Transit) train. In the area around Sungei Road, a haven for backpackers and full of hostels, I find a Hindu Temple and watch a priest remarry an elderly couple. Or are they asking forgiveness? Who knows?

The chants and incense and music make me dizzy and I cross the road for some retail therapy. The Mustafa Centre is actually retail madness. Cheap, cheap, jewellery – whole aisles of thin glitzy metal bangles, enough to cover every arm in Singapore – CDs, DVDs, watches, There are 15,000 lines, someone says. I make a promise to myself, that I'll do the more sedate (and pricier) boutiques of Orchard Road tomorrow.

I had hoped to have my fortune told by a parrot astrologer – I know, only in Singapore! Apparently the bird picks a card out of a stack and that's your future. The poor things are fed chillies to make them smarter, but today it seems they are taking a sickie. None in sight. Same with the henna painters who I'd hoped would "tattoo" my hands. So, with my hands bare and my future uncertain, I take the train again.

11.30am Sadness

Something has made me come to this place. In spite of busloads of visitors, the newly opened Changi Museum near the airport is death-quiet, and no wonder. It records the terrible time during World War II when Singapore was occupied by the Japanese. The pictures are not pretty and the stories underneath are worse. It shakes me up, and even though I know it is important, I move quickly. It's a shocking history lesson that explains Singapore another way.

12.30pm Super food

The coffee high has worn off and so it's back into town with one thing in mind. FOOD! I had wanted to try durian but it is not in season. I need to be here between June and August for that. In case you don't know, durian is a spiky football-sized fruit that smells like much-used sneakers. Locals love it, most others hate it. It is so rank that the MRT bans it, and so do hotels.

Singapore's food is a hotpot of cultures – lots of Chinese, lots of Indian and Malay, and something called Nyonya – a Chinese-Malay fusion. We try some of this in Blue Ginger at Tanjong Pagar and it's really good – banana leaf rolls stuffed with fish, beef rendang and chicken in coconut milk. We wrap up the monster lunch with bright green cendol noodles and sweet black sticky rice for dessert. Once I get over the colour, it's fine. But shame about the durian!

2pm Swinging

The Singapore Flyer is this town's newest attraction, opened March 2008. It's massive – bigger than any others around the world. We clamber into one of the 28 enclosed capsules, each of them big enough for 28 people. I struggle with the maths. How many are there each time it circuits? Too hard – I sit back and enjoy the slow and totally unscary revolution. It takes half an hour, and in that time we swing high over the (also) new Formula 1 race track, up to a bird's-eye view of the city's multi skyscrapers and the airport, and manage to glimpse two other countries – Indonesia and Malaysia!

2.45pm S$$$$s

Getting to like the MRT we hop on and head for VivoCity on the harbourfront, one of the city's best and newest shopping centres. It's massive, and it looks like every Singaporean under 25 has decided to shop here today. They're chattering in Singlish, that mix of local languages and English the locals are so proud of. Masses of bright and brief clothes in the shops – how tiny can these girls be? – sneakers, coffee shops, DVDs. VivoCity positively glows it's so shiny. Gotta go – I've walked so much my feet need some TLC and I have just heard of the ideal place.

4pm Sentosa

Lucky. The cable car to Sentosa Island is right next door to VivoCity and I hop aboard and swing out over the port, heading for Singapore's playground. Just time for a quick zip up the rotating Carlsberg Sky Tower for yet another view of the city and harbour before heading for the Underwater World spa with a Very Important appointment with some fish.

Not just any fish – these are Turkish tiddlers which actually like to nibble off the dead skin from human feet. Sounds gross, but first I have to wash my feet so they at least get clean dead skin. I am given a relaxing shoulder massage too, while I sag fully-clothed over the handlebars of something that looks like an exercise bike. Then it's off to the pool where I sit on the edge and dangle my tired tootsies in the water while dozens of tiny fish flash up to work on them. No pain, just gentle ticklish nibbles. It's called "fish reflexology" – and it works. After 20 minutes I could trek the town for another eight hours – and probably will.

Fully hyped again it's a short walk to Café del Mar right on the water's edge for an espresso and a fruit platter. I'd like to stay here all evening but there's more do.

I'm travelling with a shopping list thoughtfully provided by friends back home and I had hoped to have time to see Funan DigitalLife mall right in town – a shopping centre with seven levels dedicated to IT gadgets – but there's no time now.

6pm Sling-o'clock

It's back to my hotel, the newly refurbished and stylish Naumi Hotel, but sadly with no time for a swim. I'd checked out the infinity pool on the rooftop last night and felt I could have simply floated over the edge into Singapore's glittering nightscape. Very trippy!

For now, it's a quick change and off to the famed Raffles Hotel in the next block for an equally famous drink. I sip a Singapore Sling in the Long Bar and it's all I'd imagined, an amazing mix of gin, Cointreau, cherry brandy, Dom Benedictine, pineapple juice, Grenadine, Angostura bitters and limes. Must've been fun road-testing that one! And I make sure to add to the peanut shells on the floor. It's a good feeling. This is perhaps the only place in town that you are not only allowed, but expected, to litter.

7.30pm Safari

The MRT again comes to my rescue (although I need to bus for the last part) for a longish ride out to the zoo. The Night Safari is a world first and I grab some food while I watch a dance performance then board a tiny open-sided tram for my 45-minute encounter with nature. I'm a bit wary of this. Where are the bars and mesh fences? There are lions out there for goodness sakes! Turns out the animals are not caged, but there are deep trenches and moats that keep the human animals away from the wild ones. And vice versa. Whew! I settle down and enjoy sighting big cats and zebra and porcupines, all going about their regular night's business just metres away. It's a fabulous experience and days later I will still be talking about it.

10pm Sustenance

After all this excitement, a girl needs some First Aid and I know just where to go. Clinic Bar at trendy Clarke Wharf will dispense the exact prescription. As I settle down at a table in my gold painted wheelchair I am amazed by the tubes and glass phials at the bar and the operating theatre lights overhead. My drink comes in an IV bag, someone else sips their cocktail from a test tube. Some customers lounge back on hospital stretchers. It's crazy and not cheap – hey, good medicine always costs – and not for the squeamish. It's quite surreal, but judging by the crowds here, it works. It certainly does for me and I'm now pepped up to finish the night in style.

11pm Sashay to satays

But first a stop at the Chinatown Night Markets to line my stomach with something fried and filling. The hawkers' stalls should have just the right things I reckon. Ignoring the pretzels and wheatgrass juice, I head for Chinese cherries, four on a stick, and a handful of sizzling satay sticks _ and (yeh!) a durian spring roll. Hmmm! It doesn't smell too bad, but tastes just sweetish and unsensational. What a disappointment.

Midnight   Style Central

We catch a cab back to the waterfront and St James Power Station. It sounds pretty industrial and it's really heaving with industrial-strength energy. There are floors of rooms, nine outlets of different sizes (with just one cover charge), moody, bright, loud, with everything from jazz to Motown and mando-pop. We wander in and out, goggle-eyed, blinking in the strobe lights, window-shopping the scene.

The eateries next door are in full swing too so we refuel with barbecue at The Station Kitchen. Then it's back to St James for drinks (is there anywhere else on earth with more cocktails?) until suddenly we're exhausted.

3.30am Ssssssh!

Someone shouts in my ear that some of the late night hawker centres might still be open. "Fancy a plate of char kway teow?" they yell. Nah! Think I'll just head for the hotel. It's been a long, long day. In the taxi I groggily conclude that Singapore is more than a "fine" city. So I add one more S.

It's a Shiny city, I decide.

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Getting there: Singapore Airlines (www.singaporeair.com) flies from each major Australian city to Singapore many times a week. Singapore Airlines is the first airline to introduce iPod/iPhone connectivity – even in economy – on its newest A330-300 aircraft.

Here's a tip: check out how you can crash with the locals: Go to www.couchsurfing.org or www.hospitalityclub.org and search under Singapore.

More information: www.visitsingapore.com