Sailing, it seems, is still the preferred route for many arrivals to Sydney. It’s a tradition some 200 years old, from when the British dispatched convicts down-under-wards on a no-expenses eight-month passage aboard whichever flimsy frigate came to hand.

Today’s maritime visitors have clearly been offered an upgrade. The harbour is full of gigantic super-liners, with passengers spending less than two days ashore – a bit of change from the lifetime tariff enjoyed by their 19th century forebears.

The food and sleeping arrangements are also a notch or two up from those offered to those sheep stealers and cutpurses of yesteryear. Given the state of the modern cruise industry and today’s oceanic travel enterprises, however, it might be worth requesting some testimonials to that effect.

In truth, though, the world is now beating a path to Sydney’s door and largely on a voluntary basis, too. With the city’s look and feel soaring, the tourists have poured in. It’s a development that has delighted the locals. Whether in sport, culture or civic pride, the Aussies are a competitive and proud bunch. Nowhere is that more true than in Sydney. And so long as Sydney is beating Melbourne – at pretty much anything – that’s fair dinkum, as they say in these parts.

While both cities lay claim to being Australia’s leading metropolis, the Olympic-boost Sydney received from hosting the 2000 Games opened a gap that, as yet, shows no signs of closing. And, as Sydney-siders will inevitably ask you, just which city is home to both the iconic Opera House and the Harbour Bridge?

Those cruise visitors, then, have clearly got it all wrong. Two days is nowhere near enough to sample everything Sydney has to offer. It’s a city that should be savoured, a location you can truly immerse yourself in.

Assuming you’re not staying on a boat of any description, the choice of accommodation is endless. Business and tourist hotels abound – as well as the more funky option of a night in the likes of the QT – but Sydney is also very much an Airbnb type of place, with a wide number of rentable apartments to be had.

While location is important, so too is style. Will it be the superb Victorian suburbs of Paddington and Darlinghurst that catch your eye? Or, perhaps, the more upscale, secluded villas of Rose Bay or Surrey Hills?   Then, again, there is also the array of modern luxury apartments springing up around Darling Harbour and Walsh Bay. Wherever you choose, just make sure you’re connected to the superb local transport system – a well-planned interchange of trains, buses and ferries. A rechargeable Opal card, covering all these options, is really the first thing any visitor should invest in.

Inevitably, as with all of those cruise ships, Circular Quay will be the starting point for most tourists, with the inevitable first decision being whether or not to climb Sydney Harbour Bridge. Many do. Often at dawn, occasionally in fancy dress. In fairness, it’s a once in a lifetime experience and one that’s well within the physical capability of the vast majority of visitors.

The walks are meticulously managed, with (you’ll be glad to know) a particular emphasis on safety. Connected to a secure cable all the way to the top and back, the only risk is a touch of vertigo. There’s also “short” version of the walk – 150 minutes versus 210 – and pre-booking is pretty much essential. Oh, and don’t overdo the tinnies the night before – every would-be bridge walker is breathalysed before being allowed up.

Of course, if you opt to not walk over the bridge, you can always stroll across it, via the free-to-access pedestrian walkway. The views are just as spectacular and you still get to wave to all the cruise ship passengers. And they will all wave back.

As to what’s at the other end of the bridge, well, there’s Luna Park for a start. This is one spot where you have to spend at least half a day before you can even think about leaving Sydney. It’s one of the most quaint and old-fashioned theme parks in the world, famous for its clown’s face entrance (very Stephen King). While Luna Park may not match up to the high-octane rides of Disney or Universal, it is full of charming funfair attractions and an atmosphere that more than makes up for it.

Back across the harbour and Sydney Opera House (SOH) looks resplendent in full sail, while almost certainly waiting for you to board. As with the bridge, there is a big difference between those who actually go inside SOH as opposed to those who just have their photo taken with the unmistakable landmark in the background.

You really should make the effort to explore the interior, though, taking in a performance or just joining one of the behind-the-scenes tours. It’s not just opera. Ballet, theatre and orchestra all feature heavily in its comprehensive programme, as well as a number of contemporary music concerts. Once you’ve done that, you can then join the throng outside and enjoy the open-air bars and restaurants clustered around the most visually stunning backdrop in the world.

Keeping the Circular Quay as your orientation point, a stroll to the Botanical Gardens should be next on your to-do list. The gardens celebrate their bicentennial in 2016, two centuries of providing a rich, varied and colourful, haven of peace within the city. Follow the park round to Mrs Macquarie’s Point, a finger of land jutting into the harbour offering spectacular views of the Opera House and bridge.

As to the identity of the Mrs Macquarie in question, she was the wife of Lachlan Macquarie, Governor of New South Wales between 1810 and 1821. The couple’s influence was extensive and it was they who set about turning the crime-ridden shantytown into a modern, civilised urban development. It is thanks to the couple’s championship of culture and beauty that Macquarie is still a name that resounds across the city today.

Whether as much attention is being paid to the Macquaries’ guiding principles as the city continues to expand, though, is something of a moot point. The new Barangaroo development on the edge of the Central Business District (CBD), for instance, has met with considerable opposition from residents in Millers Point with regard to the consequent loss of social housing. Nothing, however, is standing in the way of the city’s determination to create an ambitious commercial, residential and leisure suburb in this primest of waterside locations.

It’s a process that Darling Harbour – one wharf along at Cockle Bay Point – has already undergone. Some 10 years ago this thriving area of the city was very different, with none of the apartments, restaurants and attractions that characterise it today. Now it’s an unmissable item, whether for a visit to the Maritime Museum (with its impressive replica of Captain Cook’s Endeavour), The Star complex (with its theatre and casino) or the trio of Merlin-operated attractions – Tussauds, Sea World and Wildlife.

This is where your Opal card really starts to come in handy. From Darling Harbour alone, you can enjoy ferry access to the Manly beaches, Watsons Bay and the mightily impressive Tarronga Zoo. On a Sunday, you can travel on as many ferries as you want to for less than US$1. This is why you’ll find yourself bobbing from one point of interest to another, especially if you’ve allowed yourself more than two days in town.

As with many New World cities, Sydney is very keen on its own admittedly short history, with many museums offering insights into its birth and growing pains. Recommended is the Sydney Museum, which is notably strong on Admiral Arthur Phillip’s post-1788 colonisation of Australia, the conflict with aboriginal tribes and later development of the settlement.

Equally striking – if not more so – is the Justice and Police Museum (only open on Saturday and Sunday), which provides a stark résumé of the criminal underclasses of the city in the nineteenth and early twentieth centuries. Then there’s the Hyde Park Barracks Museum, with its recreation of a prisoners’ half-way house dating back to the aforementioned Governor Macquarie’s time.

For an actual “walk through time,” though, it’s back to Circular Quay and a stroll through The Rocks, the site of the homes of the very first settler-built homes. Once notorious as a crime and disease-filled ghetto, The Rocks is now home to restaurants, bars, galleries and numerous shopping opportunities.

With the forethought to book ahead, a visit to Susannah’s Place, a preserved terrace street, provides an authentic insight into living conditions endured by Sydney families for more than 150 years.

It goes without saying, you really ought to check out what sporting events are taking place during your visit. Aussies take their sports exceptionally seriously and a trip to Sydney Cricket Ground for a Test or a Big Bash game definitely won’t disappoint. Similarly, Australian rules football will baffle and excite, while a day at the races may deplete your wallet. A game of rugby – of either code – will certainly get you fired up.

Out of town, Sydney offers another marvellous gem in the Blue Mountains, some two hours drive west. Again, no visitor should pass up an opportunity to take in the Three Sisters rock formation or a journey to the valley floor via the Katoomba Scenic funicular railway. You should also make a point of visiting the Featherdale Wildlife Park en route. Here you will get the chance to see an array of indigenous animal life in a sympathetic setting. No journey to Oz, after all, is complete without a koala-kangaroo-possum selfie.

The Australians, of course, love the outdoor life and why wouldn’t they? They are, after all, blessed with a climate that all but guarantees the hottest of summers and the mildest of winters. The top of any sun worshipper’s checklist, then, will be the renowned Bondi Beach, the legendarily expansive stretch of sand set in Sydney’s eastern suburbs. While parking may be a problem, and getting your surfboard aboard a bus is far from ideal, the locals would be outraged if you came all this way and missed the beach off your itinerary.

The barbie on the beach is a well-established Australian tradition, so join in with a bucket of prawns and a cold one if you get the chance. If you have been fortunate enough to be in Sydney on December 31, then pick your vantage point early in order to fully appreciate the 12-minute firework display that welcomes in the new year pretty much before anywhere else in the world. Except, maybe, for Melbourne and Kiribati – and those two locations are well behind Sydney in pretty much every other respect.