There is no designated wrist that a woman should wear her watch on. It is common for right-handed people to favor wearing a watch on their left wrists, as winding the clock is easier when the watch is on the non-dominant wrist. Many watches today are automatic, however, making it wholly up to the individual on which wrist he or she chooses to wear their watch.
Some people still tend to wear watches on their non-dominant hand. This is meant to avoid damaging the watch while performing common tasks like writing. Some companies make watches for people who are left-handed, so as to give them a more comfortable option of wearing their watch on their right wrist instead.