Women are not allowed to drive in Saudi Arabia. Even if you have won the desert rally or the F1 championships, it is illegal for women to drive in Saudi Arabia.
The roads are generally good, with the left hand drive, right side of the road driving system. Much of the city is built for cars, but around Masjid-al-Haram, expect heavy pedestrian movement on and off the roads. This gets even more pronounced at prayer times and at the height of the Hajj season. It is also a good idea, as is the case in most countries, to stop for pedestrians crossing the road.
In Makkah, be warned, a lot of the city is hilly with steep climbs. Traffic is okay, not very fast and not too slow. There are plenty of underpasses and bridges to take you easily around town.
Fuel is cheaper than water here, SAR 0.46 to the litre compared to SAR 1 for half a quart of water.