Remember the Middle East is not one country, one people or one culture. For example, one woman reporter in Lebanon thought she had to cover herself from head to toe in 110-degree heat because that's what women did in Saudi Arabia. That only brought her resentment from the local Lebanese people. Beirut has nude beaches. Generally, however, it's best to dress conservatively.
Women are usually OK in slacks and plain shirts.
Don't wear short shorts and halter tops unless you want to attract a lot of attention. Being a woman in the Middle East is both an advantage and a disadvantage. I remember trying to interview a government official who kept addressing himself to the male photographer who was with me. But you can impose yourself. If you show them that you're not going to be bullied by them, you'll do fine.