The birthplace of the prophet Mohammed, most visitors to Saudi Arabia come solely to visit Mecca, just inland from Jeddah. Mecca is Islam's holiest city, and all devout Muslims - wherever they live in the world - are (if possible) supposed to make the pilgrimage (or hajj) here once in their life.
Mecca and the holy sites in its immediate vicinity are off limits to non-Muslims. Apart from the obvious ideological arguments against breaking this rule, there are checkpoints along the roads to the city to stop non-Muslims from coming too close.
Although Riyadh has officially been the capital of Saudi Arabia since 1932, it played second fiddle to Jeddah until the 1970s. Built with oil boom money, Riyadh is now a technoasis of glass, steel and concrete, home to huge hotels, even larger hospitals and one of the biggest airports in the world.
The centre of Riyadh is called Al-Bathaa and is the oldest part of the city, home to the bus station and other things a traveller needs. If the city gets dull, head to the camel market for a fun out of town adventure. It's a fascinating place to wander around (despite the smell).