LHmain,
No, the ladies cannot drive legally. But look at the cars with the completely tinted front windscreens... I followed one (with a Saudi buddy) to a restaurant and a lady stepped out. It's the usual set of double standards...
I live in company provided digs. I don't have any advice for what to do when looking on your own. Ask your new boss for some advice perhaps. When you get to RUH the jungle telegraph and your buddies will sort out social life etc. for you. It's still a pretty fun place all in all.
Cheers