Riyadh and the whole of Saudi Arabia is a very conservative Muslim country. Traditional roles are highly valued, and whether you agree or not, you will be expected to follow the strict moral codes whilst traveling within the country. Men and women do not commingle much in this country. For example, museums and other sites within the city have separate operating times for men and for families. Unaccompanied women are expected to chaperoned at all times. (Chaperoning will be especially important in travel, as women are not allowed to drive cars or ride bicycles in public, making travel from one place to another quite difficult when traveling by one's self. In addition, when in public, in order to conform to local customs, women should adopt the traditional dress--clothing that is shapeless, covered by the black abaya is to be expected. Females will also want to either wear, or carry with them at all times, a veil to cover their head from their hairline. Following the local customs will help to avoid any misunderstandings, hassling, or harassment by the moral police. Long story short, take it for what it is. Following local customs will help you to have a richer cultural experience while traveling through the region.