Is it permissible for a woman to visit the holy shrines without being accompanied by her husband or a man who is related to her (Mahram)?
The key factor is that she should be secure from committing a forbidden (haram) act; yet, if she is married she should take permission from her husband. And if one of her parents or both express reasonable fear [and are anxious] about her traveling alone, she is not permitted to go against their wishes.