Sunni view: The most accepted Sunni view is that it is permissible for a women to travel alone for up to three days.
Abd Allah ibn Umar (Allah be pleased with him) narrates that the
Messenger of Allah (Allah bless him & give him peace) said: “A woman
must not travel for three days except with a Mahram”. [Sahih
Bukhari, no. 1036 & Sahih ...
Two of the popular verses that comes to mind are Al Baqarah verse 195:
And spend in the way of Allah and do not throw [yourselves] with your [own] hands into destruction [by refraining]. And do good; indeed, Allah loves the doers of good. Source: http://quran.com/2/195
and An Nisa verse 29:
O you who have believed, do not consume one another's wealth ...
it is not "going out", but it is "traveling". Women are not allowed to travel alone for long distances without mahram, and this is for her protection as you mentioned. If the travel is safe, i mean surely safe and secure, in the road, transport means , and the destination, then she may travel without mahram.
Wa Allah Aalam.
This is a ...