I lived in Riyadh until just recently and I am a western women - you can walk alone, you don't need your husband with u to go shopping - maybe years ago but not now. There are plenty of muslim women out without their husbands.

You don;t have to cover your head - unless u already do. Just make sure u carry a scarf as sometimes as women we do get asked to cover up - you will have to wear an abaya though.

If u do go out with a man - he must be a relative. You don't have to eat behind curtains in restaurants - that is your choice - but u must eat in the family section.

I loved Riyadh and I wld go back tomorrow. Shopping is fabulous compared to Doha - 90% off sales - amazing , and sooo much variety compared to here.

Eating out is so cheap also and loads of variety to choose from.

Hope this helps.