Although it is not compulsory for women to cover their hair or wear an abaya anymore, it is recommended to dress modestly. Long years of tradition make changes standing out. If you want to avoid looks, just try to dress covering your legs and shoulders (although as we said before, it is not mandatory) and avoid tight clothes.
Abaya: loose garment robe-like dresses that covers the whole body except the head, feet and hands.
It is completely allowed to use bikinis and swimming suits at private beaches. Their use at public beaches is not forbidden but not very recommendable as you will get some looks, specially in remote locations.
Women over 21 years old can travel abroad and throughout the country on their own. In general terms, many regulations are changing in favor of women. Women already have the right to register their children´s births, as well as marriages or divorces, working opportunities are expanding for women and we can officially drive since September 2017.