A first week in Saudi Arabia

You are met at the airport in Riyadh and taken to your hotel. Riyadh is the country's main air hub, so it is usually the arrival point whether or not the capital is the reason for the trip.

Nothing is scheduled for the rest of the day. Distances inside the city are large and it is built for driving, so a car and driver are on call if you want to go out.

The morning is at the National Museum of Saudi Arabia, arranged as halls that run in order: geology, pre-Islamic Arabia, the life of the Prophet, the successive Saudi states and the unification. The whole span can be walked in one visit without doubling back. Large bags go into lockers at the entrance, as some halls restrict oversized belongings.

In the afternoon, Al Masmak, the mud-and-clay fort in the old centre where the capture of Riyadh in 1902 began the state that exists today. Four watchtowers, thick clay walls and a single studded door with a spear tip still lodged in it. It stands on the same ground as the museum, so the two work as one half-day rather than two separate outings.

About twenty minutes from central Riyadh, At-Turaif was the seat of the Emirate of Diriyah from 1727 to 1818 and has been on the UNESCO World Heritage List since 2010. It has been restored and opened as a museum quarter, so you walk the streets rather than a perimeter: thick mud-brick walls in the Najdi style, stepped parapets, and triangular openings cut high for light and air.

Wadi Hanifa runs directly below the district, reclaimed from a dumping ground into a green corridor with walking paths along the streambed. The day ends there, then in the restaurant and cafe quarter beside At-Turaif.

Morning flight to AlUla, a sandstone valley that was farmed and settled for thousands of years because it has water, and sat on the incense road running north out of southern Arabia. You are taken to your hotel and the middle of the day is free.

Late in the afternoon you drive out to Elephant Rock, a 52-metre sandstone outcrop weathered into the shape of an elephant with its trunk to the ground, twenty minutes north-east of the old town. Sunken seating has been cut into the sand around the base; the stone turns deep red as the light drops. There is no entry ticket.

Hegra is the largest surviving Nabataean city after Petra and the first place in Saudi Arabia inscribed on the UNESCO World Heritage List. More than 110 tombs are cut into sandstone outcrops standing on open desert floor, their facades carved directly into the rock.

The site is entered only on a guided tour with an AlUla Rawi, the local storyteller-guides, moving between tomb clusters by vehicle. Numbers each day are capped, so the booking is made before you travel rather than on arrival. At the visitor centre is the reconstruction of Hinat, a Nabataean woman whose burial was excavated in 2008.

The morning is at Dadan, capital of the Dadanite and Lihyanite kingdoms, where the tombs are cut almost 50 metres up the cliff wall as square openings in a line, two of them guarded by carved lions. Excavation is ongoing and a good deal of the site is still unread.

Then Jabal Ikmah, a short desert canyon whose walls carry hundreds of pre-Arabic inscriptions in Dadanitic, Thamudic, Minaic and Nabataean script. It was added to UNESCO's Memory of the World Register, which covers documentary heritage and is a different list from the World Heritage List. The path is level and there is no ticket. Evening flight on to Jeddah.

Historic Jeddah, known locally as Al-Balad, has been on the UNESCO World Heritage List since 2014. Jeddah has been a major Indian Ocean port since the 7th century AD and the sea gateway for pilgrims to Makkah, and that double role paid for the quarter that survives: tower houses of coral stone several storeys high, faced with roshan, the carved wooden bay windows that let air through while keeping the street from seeing in.

Much of the quarter is propped and under restoration, building by building, so it reads as half ruin and half work site. You are taken to the airport in time for your flight out.