The suggestions already given are correct, think modesty with a capital M and absolutely nothing skin tight (such as current western fashions). Think loose and totally covered neckline, legs, arms.

I traveled to Egypt alone in my twenties and was groped by guides in the museums, most unpleasant. It's the only place I've ever traveled where I felt it necessary to attach myself to a western couple for my own safety.

Other helpful items would be an umbrella (sun protection), sunscreen, hat, tiny battery-operated personal fan, purse worn with diagonal strap across the body, and be sure to take a flashlight for viewing wall paintings inside tombs.

Even with some personal harrassment, Egypt was a highlight of all my lifetime of travels. Enjoy.