Three UNESCO sites in one journey

Riyadh is the country's main air hub, so it is usually the way into Saudi Arabia whether or not it is the reason for the trip. You are met at the airport and taken to your hotel. Nothing is scheduled for the rest of the day.

The morning is at the National Museum of Saudi Arabia, arranged as a sequence of halls that run in order - geology, pre-Islamic Arabia, the life of the Prophet, the successive Saudi states, unification - so the whole span can be walked without doubling back. It makes the sites later in the week easier to read.

In the afternoon you cross to Al Masmak, the mud-and-clay fort where the capture of the city in 1902 began the state that exists today. Four watchtowers, thick clay walls, a single studded door. Both sit in the old centre, which makes the two a single half-day rather than two outings.

About twenty minutes from central Riyadh, At-Turaif is the mud-brick district that served as the capital of the first Saudi state, and a World Heritage Site since 2010. The Emirate of Diriyah ran from here between 1727 and 1818. It is the most complete Najdi architecture at this scale anywhere: thick walls, stepped parapets, triangular openings cut high for light and air. The district has been restored and opened as a museum quarter, so you walk through the streets rather than around a fence.

Wadi Hanifa runs directly below it - the valley that carried the water Riyadh grew on, reclaimed from a dumping ground into a chain of parks and water channels. There is a restaurant and cafe area alongside the district, so the day runs into the evening.

You travel north to Hail, northern desert country of granite ranges, old forts and rock art. The afternoon is in the Aja mountains west of the city: dark red granite standing straight out of pale Nafud sand, with palm settlements in the gaps between the ridges. The rock reads almost purple at either end of the day, which is the reason for going late rather than at noon. A'arif Fort and Barzan Palace are in the city itself if there is time on the way back.

Jubbah lies about 90 km north-west of Hail city, out in the Nafud sand sea, so it is a half-day at minimum and is given a whole one. The carvings at Umm Senman are cut into sandstone that once stood on the shore of a lake, and they show human figures, cattle, ibex and hunting scenes. The animals belong to a wetter Arabia than the one around the rock today, which is what gives the site its value - it is a dated record of the climate changing. UNESCO inscribed the Hail rock art in 2015.

You travel west to AlUla, a sandstone valley that was farmed and settled for thousands of years because it has water, and that sat on the incense road running north out of southern Arabia. The afternoon is left open.

In the evening you walk AlUla Old Town, a labyrinth of mud-brick houses built from the 12th century, walled and once entered through fourteen gates, abandoned within living memory and now partly restored. The restored lane of shops and restaurants runs late, which makes it the one place in the valley with a real evening.

Hegra is the largest surviving Nabataean city after Petra and the first place in Saudi Arabia to be inscribed on the World Heritage List. More than 110 tombs are cut into sandstone outcrops across the desert floor, their facades carved directly into the rock. Access is by guided tour with an AlUla Rawi, one of the local storyteller-guides, moving between the tomb clusters by vehicle; daily numbers are capped and your place is booked before you travel. At the visitor centre is the reconstruction of Hinat's face, from a burial excavated in 2008.

Later you stop at Dadan, capital of the Dadanite and Lihyanite kingdoms, where the tombs sit almost 50 metres up the cliff face as square openings in a line, two of them guarded by carved lions. The day ends at Jabal Ikmah, a canyon whose walls carry hundreds of pre-Arabic inscriptions - closer to a public noticeboard left open for two and a half thousand years than a monument.

Mornings here are cool and the light is low, so if your flight allows there is time for Elephant Rock, a 52-metre sandstone outcrop weathered into the shape of an elephant with its trunk to the ground, standing alone on open sand. You are then collected from your hotel and transferred for your flight out.