Nine days from Dubai to Musandam: Arabia has fjords, and almost nobody goes

Dubai International is close to the old town and about forty minutes from the Marina end of the city; the red metro line runs from inside the terminal and is the cheapest way in by a wide margin.

Give the first evening to the Marina, which is a three kilometre canal cut inland and ringed with towers, with a walkway the whole way round. It was desert twenty five years ago, which is the fact that makes it interesting rather than the towers themselves.

Eat on the walkway, and go to bed early enough to start properly tomorrow.

The Museum of the Future is a torus of steel and glass with Arabic calligraphy cut through its skin, standing on Sheikh Zayed Road, and it is the best looking building in the city. What is inside divides people sharply: it is closer to an art installation about the next fifty years than to a museum, and the tickets are timed and sell out.

Then Jumeirah Beach for the middle of the day. The public stretch is free, has showers and cafes behind it, and looks straight across at the Burj al-Arab on its own artificial island, which is the view every photograph of Dubai used before the Burj Khalifa existed.

In the late afternoon go out onto the Palm. The View at the top of the tower on the trunk is the only place you can actually see the shape of the thing, because from the ground it just looks like a suburb.

An hour and a quarter up the coast, through Sharjah and Ajman, and the towers stop somewhere around Umm al Quwain. Pick up the hire car in Dubai for these two days if you want one; it is the only stretch of this trip where driving yourself is straightforward.

Stop on the way at Al Jazirah al Hamra, a pearling and fishing village of coral block houses, a mosque and a market, abandoned in the 1960s and left standing. It is the best preserved village of its kind in the Emirates, and walking through the roofless rooms with the wind going through them is a strange corrective to the morning you have just had.

In the town itself, the national museum is inside Al Hisn fort, which was the ruling family's residence, and covers the emirate's archaeology, pearling and the treaties of the 19th century. An hour, and it puts names on everything you will see tomorrow.

The road up Jebel Jais is thirty odd kilometres of engineered switchbacks climbing to about the highest point you can drive to in the Emirates, and the mountain tops out at 1,934 metres. There are viewing platforms at intervals, a restaurant near the top, and the longest zip line in the world strung down the face of it if that is the sort of thing you do.

Go early. The morning air is clear and by afternoon the haze from the coast usually fills the valleys below you.

On the way back down, turn off for Dhayah, where the only hilltop fort left in the Emirates sits on a mound above the palm gardens. The hill has been occupied since the Bronze Age and the fort on top of it was the last position to hold out when the British attacked in 1819. It is a steep ten minutes up and the view runs from the mountains to the sea.

Two hours north, and the last hour is the reason to do it in daylight. The road hugs the coast on a shelf blasted out of the cliff, with the sea directly below and the mountain wall directly above, and there is nothing built along it.

The border at Tibat is small and usually quiet. Have the passport ready, expect a few questions and a stamp, and remember that this is a real international frontier and not a checkpoint. Your driver will wait.

Khasab appears in a bowl of date palms at the head of its own bay. Spend the afternoon at the castle, a low square Portuguese fort of the early 17th century with a round tower in the middle of the courtyard, which later housed the local governor and now holds the town's museum. Then walk the old souk for the carved walking sticks that Musandam men still carry.

The full day cruise is the thing people come to Musandam for, and it is worth taking over the shorter version. A motorised wooden dhow leaves the harbour in the morning, loaded with rugs and cushions, and turns into Khor Ash Sham, the longest of the inlets, with grey cliffs going up on both sides straight out of the water.

Dolphins usually appear within the first half hour and often ride the bow. Halfway in, the boat stops at Telegraph Island, a rock in the middle of the fjord where the British built a telegraph repeater station in the 1860s and abandoned it four years later. The story that the phrase about going round the bend comes from the sail back out of here is probably not true and is told on every boat.

You anchor for a couple of hours to swim and snorkel, eat lunch on the deck, and come back in the afternoon past a village or two that has no road to it. Take a windproof layer: the deck is colder than the town.

A four wheel drive day into the mountains, arranged the night before, climbing a graded track from sea level to about two thousand metres in an hour and a half. The road passes terraced villages, stone shelters and a plateau where the wind has scoured the ground flat.

Jebel Harim is the roof of Musandam, and the fact worth carrying up there is that the limestone at the top is full of marine fossils: the whole peninsula was seabed, and it is still tilting, which is why the valleys are drowned and the coast has fjords in the first place.

Come down in the late afternoon and go to the harbour. The dhow port is photogenic at any hour, but at dusk the small fast boats that run livestock and goods across the strait to Iran are being loaded, and it is the most purposeful thing happening in Musandam.

Three and a half hours back to Dubai, the same road in reverse and the same border, and the cliff section is worth staying awake for a second time. Aim to be in the city by mid afternoon.

The last evening is the one for the tower. The Burj Khalifa is 828 metres and 160 floors, finished in 2010, and the public deck is on the 124th; book the slot online days ahead because the walk up price is punishing and sunset slots go first.

Then go down to the lake below it for the fountain, which runs every half hour after dark, is free, and is a better spectacle than anything you paid for that day.

Dubai International is fifteen minutes from the creek on the metro, which makes a late flight easy and an early one manageable.

If there is a morning, spend it in Al Fahidi, the surviving pocket of old courtyard houses with wind towers on their roofs, and take an abra across the creek and back for the price of a coin. It is the oldest thing in the city and the cheapest, and it makes a better last impression than the airport lounge.