For a panoramic view over the city, visit Cerro Santa Lucía, a central, rather romantic park. For even more panoramic vistas, a cable car leads to the summit of San Cristóbal, where you can join Chilean families wandering along the leafy paths. Afterwards, have a beer at one of the pavement cafés in Bellavista. This is an Italian quarter of narrow streets peppered with bars and shops selling local lapis lazuli (only Chile and Afghanistan produce the stones in commercial quantities).

The museum and house of Chilean poet laureate Pablo Neruda is close by, and its unusual interior with an eclectic collection of paintings and bric-a-brac is well worth a visit.

Punta Arenas was an important, British-influenced trading centre before the opening of the Panama Canal turned it into a backwater; the region's fortunes were only briefly revived during a short-lived gold rush. To add to its woes, the sheep-rearing business has never recovered from the catastrophic collapse of the price of meat and wool. No pure-blooded indigenous people are left alive here; having survived for centuries the rigours of the Antarctic climate they were annihilated by the diseases brought in by sailors and missionaries at the turn of the 20th century. Overnight in the city.

Stay in one of the cosiest and best located lodges within the park. There are views of the towering granite massif from the property. Your time here allows you to explore extensively, on foot and by boat, and to enjoy the peace and beauty of this national park, deservedly one of South America's most acclaimed attractions.

The park authorities have been sensitive about keeping the site as natural as possible, and there are no shops or cafés within close proximity of the wooden viewing platforms, which are landscaped into the cliff. Just looking at the cliff-edge of the glacier, which towers 60m above the water surface and is an extraordinary 5km wide, is awe-inspiring in itself. But after a time you hear the unforgettable sound of the glacier calving a vast wedge of ice the size of a tower block and sending it smashing down into the lake, where it divides and floats away as an iceberg.

There is an optional mini-trek on the glacier (local regulations enforce a maximum 65 yrs of age policy). Walking out on the ice is an extraordinary experience; atop this immense ice sheet you feel exposed to the elements, and you can explore the craggy, desolate landscape, peering into crevasses and deep water pools, squinting against the incredible blue of the ice. It is a 1-2 hour walk on the ice led by a local guide, and crampons are provided.

The world's southernmost city, Ushuaia sits at the foot of a hand of jagged peaks. Thus isolated, it was a penal colony at the turn of the 20th century and a sleepy frontier town until the late 1970s when it was turned into a tax haven to encourage settlers. Immigration has slackened off nowadays as this status is being rescinded but effects of the boom are nonetheless evident, with chalet-style residences, modern hi- tech factories, shopping malls and duty free shops.

During your stay there is a boat trip along the Beagle Channel, named after the ship carrying Charles Darwin’s scientific expedition which travelled these waters. The vessel heads out of Ushuaia Bay to explore the bays and islets of the channel, and there are brief stops for you to get a closer look at some of the fauna, which includes cormorants, sea-lions and penguins. If you are lucky you may even catch a glimpse of an albatross gliding over the water.

To take a break from the city’s frenzy, you can travel by motor catamaran across the River Plate border to Colonia in Uruguay (don't forget your passport) where you can wander cobbled streets and admire the squat colonial houses from the top of the lighthouse, and have a glass of wine or lunch in the yacht club.

Wherever you are on your last day, if you are an enthusiastic carnivore make sure you have a juicy steak, usually up to a quarter of the price of its UK equivalent. Finally you could catch a tango show for a fantastic farewell to the city.