When you're shopping along Orchard Road, or admiring the new, futuristic Gardens by the Bay attraction, it's easy to forget that Singapore was smothered in wild, swampy jungle not so long ago.
Yet while the city-state's rapid modernisation has been startling (and ongoing), its earthy origins haven't completely vanished.
At the centre of Singapore, the Bukit Timah Nature Reserve grants a glimpse of what things were like when the British colonialists, led by Stamford Raffles, arrived in 1819.
Blessed with hilly walking trails, this muggy urban rainforest lies south of Singapore Zoo and the Night Safari Park, where you can eye nocturnal animals, including the kind of tigers that once roamed freely here.
To really get off the beaten Singapore track, however, I've decided to hop off the "Mother Island" and explore some of the city-state's offshore nuggets.
There are 63 Singaporean islands in total. Some are out of bounds, notably Jurong, which is strewn with petro-chemical plants, and Tekong, a military training base. Incidentally, Christmas Island (1300km south of Orchard Road) was part of Singapore before being sold to Australia in 1957.
From Marina South Pier terminal, close to the flashy Marina Bay Sands casino and resort, I board a small passenger boat to St John's Island.
We're soon drifting past Sentosa, the most developed of Singapore's outlying islands, and a haven of five-star hotels, multi-million-dollar apartments and family entertainment, including the world's biggest aquarium.
About 20 minutes later, we pull in at St John's, which was formerly a quarantine site for immigrants suffering from cholera and leprosy, then a prison for political detainees and a rehabilitation centre for opium addicts.
These days, it's set up for picnicking, undulating woodland walks and camping. Outside of weekends and public holidays, you can virtually have St John's to yourself.
Blissfully free of hooting traffic, on my visit the island's loudest noises come from meowing cats and myna birds squabbling amid the rustling branches of casuarina trees.
The only other humans I see are groundkeepers and staff from the island's marine science research centre (which holds occasional public open days).
Sedate St John's is linked by a causeway to Lazarus, an even more laid-back island, which is edged by the type of unspoilt white-sand bays and calm emerald waters common in Indonesia. You can see glimpses of the Indonesian archipelago from the causeway.
Across a current-prone channel - and accessible via a short boat ride from St John's - Kusu Island is shrouded in spirituality.
Shrines to Malay saints crown a leafy hillock at the heart of the island, and by the waterfront, two Taoist deities are revered at the Da Bo Gong Temple, which draws thousands of worshippers for its annual pilgrimage (in 2013, October 15 to November 13).
In Chinese, Kusu means tortoise. According to legend, the island was created by a magical tortoise to save two shipwrecked sailors.
Dozens of tortoises swim and frolic in the island's refuge pool, and you may spot some out in the wild if you snorkel in the lagoons.
I take a breather on one of Kusu's picnic benches and stare back over the water at Singapore's burgeoning skyline.
In the foreground, giant freighters sluggishly advance to dock at the world's busiest shipping port.
I wonder what Singapore will be like in the decades to come. The Singaporean government has announced controversial proposals to boost the city-state's population from 5 million to 6.9 million by 2030 - and opponents fear over-development, all over.
A few peaceful hours later, I'm boarding a boat back to the Mother Island, but the next day I savour another rustic slice of Singapore on Pulau Ubin, a beguilingly sleepy rural backwater that's a 10-minute bumboat (water taxi) ride from Changi Point ferry terminal, close to Changi International Airport.
Stretching 8km east to west, and about 2km at its chunkiest point, boomerang-shaped Ubin was first mapped by the British in 1828. In the Malay language historically used in Singapore, Pulau Ubin means granite island, and its natural resources were mined to construct lighthouses and, later, the first causeway bridging Singapore and Malaysia.
Although Ubin is bigger than St John's, Lazarus and Kusu combined, you can cover it, in half a day, on a bicycle via a series of interlocking paved roads and gravel tracks, which are lined with forests teeming with coconuts, jackfruits and sweet bananas.
Ubin is home to about 100 people. They mostly earn a living from fishing and farming, selling food and drink, and hiring bicycles to tourists and mainlanders, who flock over on weekends.
Pedalling, languidly, around the island, I dodge the kind of wildlife you wouldn't expect to see in Singapore CBD: a wild boar, a slithering black snake, long-tailed monkeys and a pack of docile stray dogs.
I pass tiny kampungs: villages of wooden, zinc-roofed shacks home to Ubin's (largely elderly) population (Singaporeans of Chinese and Malay descent).
I pause at a mock-Tudor timber-framed cottage built in the 1930s as a holiday retreat for the chief British surveyor and later converted into a visitor centre for Chek Jawa, a network of tidal wetlands. They were discovered almost by accident in the late 1990s when the government announced plans to reclaim, and develop, the land.
After a biodiversity study revealed a wealth of wildlife-rich ecosystems, the idea was shelved. Treading Chek Jawa's tree-shaded boardwalk, I look down to see crabs, shrimps and salamanders scampering in the puddle-strewn mangroves.
Overlooking the forest canopy, a lofty wooden viewing tower gives bird-watchers the chance to spot collared kingfishers, oriental pied hornbills and white-bellied seagulls - as well as the winged marvels rising from Changi Airport.
Back in Ubin's main town - just a small cluster of family-run stores and restaurants - you can sample typical Chinese and Malay rice and noodle fare, and some terrific seafood.
At Celestial, the island's sole resort - a rustic hideaway a five-minute amble from the town - I enjoy a sumptuous lunch of steamed sea bass and salted egg prawns, and a conversation with a few Singaporeans who've come over from the Mother Island.
Revelling in the placid ambience, and their chilled Tiger beers, they express one sentiment time and again: "Ubin feels like Singapore 30 years ago - just like when we were kids."
To visit Pulau Ubin, 12-seater boats leave Changi Point Ferry Terminal when full; S$2.50 ($2.15) each way. For St John's and Kusu islands, it's $12.70 for a day-travel ticket. Boats leave Marina South Pier at 10am and 2pm weekdays (more on weekends and holidays). islandcruise.com.sg.
In a row of revamped former shophouses, the Sultan Hotel is a great place from which to explore. This new 64-room boutique hotel is in Kampong Glam, a neighbourhood that bloomed with Arab traders and Malay aristocracy after Stamford Raffles signed a trade treaty with Singapore's sultan in 1822. Rooms from around $158. thesultan.com.sg.
At the Celestial Resort on Pulau Ubin, rooms cost from $143 and villas are from $255. ubinbeach.celestialresort.com.
See yoursingapore.com.Steve McKenna was a guest of the Singapore Tourist Board.