We wanted to see what riding in the city was like and it is tough. This is a car-central country. Every part of the city is designed around cars. You need a bit of fatalism to cycle out into your lane.
On the other hand, it seems quite safe. We went into a restaurant for over an hour and left our bikes, parked out fronton the proprietor's suggestion, without being locked and they were just fine.
But I would skip the city part of the ride and start on the peripheral loop. Riding uphill on route 267 there is a broad shoulder. Of course, cars and trucks use the shoulder in Saudi Arabia, but they're typically slow enough and should see you cycling there. There are sections of old road and sections of gravel paralleling the road, but they are incomplete.
The Al Wuhait road is a delightful ride, with low automotive traffic and pleasant desert scenery. Camels, horses and people out in their fields. Then some 4x4 territory along the wadi.