What is the role of women in Romeo and Juliet?

As so often in Shakespeare (this being one of the many reasons we love his plays), in Romeo and Juliet Shakespeare shows strong, resourceful women who often show more sense than the men.
If we turn to the young Juliet, who clearly has the major female role in the play, we find a strong, resourceful woman (or girl—she has not yet turned 14). She knows her own mind, and she is just as impatient as Romeo to get married. She is also very passionately in love. However, unlike Romeo, she shows a more acute awareness of the danger surrounding their situation as part of two feuding families. For example, she keeps urging Romeo to leave his post under her balcony for fear he will get killed by her male relatives if discovered, and it is she who insists he leave their marriage bed for the same reason. Romeo, as always, would push things past their limits.
Shakespeare also uses women to show the effects of male violence. In this play, as so often in life, it is the men who fight and the women who grieve the outcomes of the fighting or try to prevent the violence for fear of the outcome. We see, for example, Juliet's father, Lord Capulet, dashing off delighted and gung-ho to a street brawl early on in the play while his wife, more attuned to the dangers, tries to stop him. Likewise, Romeo kills Juliet's beloved cousin Tybalt (and we understand why—Tybalt has killed no less than the vibrant, dynamic Mercutio who Romeo loved)—but Juliet articulates the pain Tybalt's death brings her in a moment of deep anguish as she contemplates it is the person she loves who has killed the person she loved.
The Nurse, too, expresses anguish over Tybalt's death:

O Tybalt, Tybalt, the best friend I had!
O courteous Tybalt! Honest gentleman!
That ever I should live to see thee dead.

The Nurse displays loyalty to Juliet and perhaps a shrewd wisdom in trying to slow her down in her passions. When the Nurse comes back from her meeting with the Friar about the wedding, she takes her time communicating her information to the frantic Juliet—suggesting that it might be a good idea overall for the couple to slow down. When Mercutio, still very much alive, teases her about being involved in prostitution, the Nurse does not laugh but gets angry, revealing that men and women have different reactions to the same topic.
As he often does, Shakespeare illustrates in this play that the women often have more sense than the men.