Melbourne may not have a coliseum or a carnival, but it is still packed with great days out that are unique to the city, writes Stephanie Bunbury.

So you've been to see the penguin parade. You've had coffee in Carlton. Maybe you have gone down the Great Ocean Road for a couple of days – not that seeing those waves smashing on the southern edge of the continent ever gets old, exactly, but you have ticked it off the metaphorical list. So where do you take your visitors next? We are all very much aware of Melbourne's status as the world's most liveable city. But how visitable is it? How holidayable? Without a Coliseum, a Tower of London or a Rio-style carnival?

Melbourne has about 2 million tourists a year, about one-third of whom come to visit family or expatriated friends and thus may well have been here before. I live in London, but come back every year for a couple of months. What strikes me is that Melbourne doesn't actually offer much to visitors in the way of sights. It's a city of days out: days spent cycling, walking, ambling or simply hanging out, the kind of place where visitors will go home saying "Remember that picnic? With those cockatoos that tried to eat our sandwiches? That was a really great day."

TALK TO THE ANIMALS

A lot of people's first introduction to things Australian is a toy koala. Foreigners love our funny animals, as evidenced by their eagerness to be photographed holding them (Louise Brooks, Barack Obama) and the world cult surrounding Steve Irwin. You will probably already have taken your visitors to Healesville Sanctuary and down the Great Ocean Road to go koala-spotting at Kennett River, where our sleepiest furries can be seen slowly munching lunch in every second tree. But there are wild animals closer to home: try possum-spotting in the Fitzroy Gardens at night or go down to St Kilda Pier in the evening to see little penguins frolic.

An easily manageable day trip to Werribee Gorge (62 kilometres from the city, offering shorter "family" walks and, for the reasonably fit, a 10km circuit) gives a good chance of seeing lots of water birds and black wallabies on the hop; this is not to be confused with Werribee proper, where visitors can toggle between the gracious Werribee mansion and its English-style gardens (8734 5100/ bookingswerribee@parks.vic.gov.au) and the excellent Werribee Open Range Zoo featuring African animals. And don't forget the Melbourne Zoo, with its beautifully designed habitats, twilight concerts and expensive but exciting Roar 'n' Snore camping nights. (Bookings for both zoos 1300 966 784).

If Melbourne means anything, it means not having to queue for a decent cup of coffee.

THE GREAT OUTDOORS

This is the other reason visitors come here. Some of us are old enough to remember when the city fenced off its river frontage; when there were hardly any walking paths, let alone cycling paths. Now you can cycle from the Dandenongs to the city without hitting a road. Your European visitors will probably be used to walking: take them by train down to Altona, walk along the Hobson's Bay Trail past the kite-surfers to the seemingly endless wetland spaces of Cheetham. Or walk the other direction to villagey Williamstown (about 5km) and then on to the excellent Scienceworks museum (a further 3km) from where, if you're there during early morning or late afternoon, you can get a punt across to more wetlands and the start of the Capital City Trail under the Westgate Bridge. There are also trains or the ferry – fun for guests – that takes about an hour to chug between Southbank and Williamstown; times depend on passenger numbers and tides, so ask ahead on 8610 2600.

On the other side of town, the coastal pathways between St Kilda Beach and Sandringham make a good day walk (about 16km); you can keep going for longer, obviously, or just do shorter sections, coming back to the city on the Sandringham line from any of the Brighton stations. Many of these beaches are patronised largely by locals and look much the same as they did in the paintings by Australian impressionists reproduced on the information boards along the way.

American visitors may well be impressed by the strip shopping centres – Elsternwick's Glenhuntly Road is a good example – with verandahs over the footpaths and the kind of independent mom-and-pop shops that have all but disappeared from Main Street USA. And visitors of every stripe will be delighted by the Botanic Gardens, a unique oasis of tranquillity free to us all, or a trip to Yarra Bend Park (bus 200 or 207) where you can eat at the historic Studley Park boathouse or take a picnic and hire a rowboat to find your own spot on the river.


EMBRACE YOUR INNER DAG

Explain to your visitors, if you can, what the word "dag" means. Then book them on to the Restaurant Tram. Don't worry if you think it's the last thing on earth you would want to do. It's fun, especially for people who come from some city where they don't have trams. The street's-eye view gives an entirely different view of the city. Or do a little garden tour of the arrestingly off-kilter Kennedy Memorial in the Treasury Gardens, followed by the adorably twee Model Tudor Village in the Fitzroy Gardens. Later on, find a karaoke bar in Little Bourke Street and let loose Donna Summer at double speed, set to videos of languid romantic couples shot in Hong Kong. This is who we are.

LOOKING DOWN

Talking of different views of the city, check it out from the 88-storey Eureka Skydeck on Southbank. At $19.50 for an adult, it's kind of pricey for just having a look at things. But, according to architect Karl Fender in his contribution to the My Secret Melbourne column in this paper, his Asian visitors love it. "When they're up there, they're knocked out, because Melbourne is a beautiful city. They don't understand that we're so close to the vineyards of the Yarra Valley and the beaches." (www.eurekaskydeck.com.au/9693 8888) Of course, you can see much of this for the price of a top-end drink – about the same as the Skydeck, as it happens – from the Lui bar in the Rialto Tower on Collins Street (55 storeys; strict dress code; no bookings; you have to be buzzed in once approved). Or take a lift to the 35th floor of the Sofitel at the top end of Collins Street (where nobody buzzes you), visit the toilets and take in the magnificent floor-to-ceiling view out to the Dandenongs for absolutely zilch. Then, while you're there, you may as well have a cocktail, no?

LOOKING UP

At one time, it seemed the whole of Melbourne – at one time, thanks to the flush of gold rush money, a bandbox example of 19th-century town planning – was going to be torn down in the name of progress. All things considered, it's astonishing how much has survived: the ornate Victorian Gothic banks at the bottom end of Collins Street, the recently buffed art nouveau tile work on the fascia of David Jones (once Buckley and Nunn) in Bourke Street, the deco glories of the Manchester Unity building. Just out of the CBD in Albert Street, East Melbourne is the fire station featuring Harold Freedman's mosaic depicting Prometheus' theft of fire from the gods, a personal favourite. It dates back only to 1982, but is very much in the spirit of Marvellous Melbourne. From there, it's just a hop and a skip to the specifically Melburnian version of hipster central: Brunswick Street. (See also Sydney Road, Brunswick; Smith Street, Collingwood; or High Street, Northcote.) It's a flaneur's paradise.

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Link Daggy: Just because you wouldn't be seen dead in the Restaurant Tram doesn't mean your guests wouldn't love it. Photo: Andrew De La Rue

WHICH LEADS US, INEVITABLY, TO …

"Don't talk about the laneways," groaned one friend. "Everyone talks about the laneways." Well, of course they do: they are everyone's idea of what a city should and could be and it's pretty much only Melbourne that has them. There are enthusiastic young persons painting the walls; there's coffee and noodles; there are funny little shops where you can get a zip put into your skirt for 10 bucks; there are bars so cool they don't have names. What's not to like? Degraves Street used to be just a quick way to get to the railway station; look at it now! The Block Arcade is more beautiful than ever. Just don't give in to your visitors' insistence on visiting the admittedly glorious Hopetoun Tea Rooms, which must be in every guidebook to Melbourne judging by its permanent queue of eager tourists. Ridiculous. If Melbourne means anything, it means not having to queue for a decent cup of coffee. For which we must make mention of the great coffee-and-pasta original: Pellegrini's on the corner of little Crossley Street at the top of Bourke, where you can be lucky enough to sit at the group table in the kitchen and pretend you're at Nonna's somewhere in Italy.

INSIDE STOREYS

It isn't only the exteriors of Melbourne's trove of old buildings that have been preserved. Theatres and cinemas have fared surprisingly well, despite long periods of closure (the Regent on Collins Street, with its mediaeval fairy-tale interior), controversial redevelopment plans (the Forum, built in 1929 to look like something from the Arabian Nights as re-imagined by Jay Gatsby's party planner and now under renovation; see also the Palais in St Kilda); and only intermittent theatrical ventures (the graciously classicist Athenaeum, built in the 1870s, full of wall reliefs of reclining nymphs). Whatever they're showing, these are beautiful ambassadors of their respective eras.

As are Melbourne's quite remarkable number of preserved art deco cinemas: the grandly shabby Astor in Windsor, the Palace chain's Westgarth in Northcote, the Classic in Elsternwick with its downstairs restaurant, the fabulously eccentric Sun Cinema in Yarraville and the gracious Rivoli in Camberwell. Camberwell is not the sort of place you might consider a day out, but you could unite a trip to the movies with a morning at the Camberwell Market. "Everyone likes a rummage," says my friend Steve. "And you will always find something in a foreign country you would never see at home."

QUIET TIMES

Help your chums take the weight off those sight-seeing feet at the State Library, with its reading dome-lit with green baize lamps redolent of the old British Library and Ned Kelly's armour on show in the museum next door. the private Athenaeum library above the aforementioned theatre; or various of the city's churches. Evensong at St Paul's Cathedral, where you can listen to the choir lift its venerable roof, is a restful alternative to the beer-o'clock drink. Or take a walk past the rainy window to the Shrine of Remembrance, the one thing in Melbourne that is really impressively monumental in the manner of Napoleon's Tomb in Paris or the Statue of Liberty. Stand on the steps and look back at the city. It's just the place for a holiday.