Can she travel without a mahram to visit her parents?

It is not permissible for a woman to travel without a mahram,
whether she is travelling to do an act of worship such as Hajj or visiting
her parents in order to honour them and be kind to them, or travelling for
permissible purposes such as going on vacation etc. The evidence for that is
as follows: 

1 – The general meaning of the words of the Prophet
(peace and blessings of Allaah be upon him): “No woman should travel unless
she has a mahram with her, and no man should enter upon her unless her
mahram is present.”  A man stood up and said: “O Messenger of Allaah, my
wife has gone out for Hajj, and I want to go out with such and such an
army.” He said: “Go and do Hajj with your wife.” Narrated by al-Bukhaari,
1862. 

Muslim (1339) narrated from Abu Hurayrah that the Prophet
(peace and blessings of Allaah be upon him) said: “It is not
permissible for a woman who believes in Allaah and the Last Day to travel
one day’s distance without a mahram.” There are many ahaadeeth which forbid
a woman to travel without a mahram; they are general in meaning and apply to
all kinds of travel. 

2 – It is well known that travel involves exhaustion and
difficulty. Because of her weakness, a woman needs someone to help her and
look after her. Things may happen to her that make her panic and act out of
character if there is no mahram present. This is well known nowadays when
there are so many car accidents and other kinds of transportation accidents.
Moreover, travelling alone exposes her to temptation, especially since there
is so much corruption. Men who do not fear Allaah may sit neat her, and
haraam actions may become attractive to her. Similarly if she is travelling
alone in her car, she is exposed to other kinds of danger, if the car breaks
down or if evil people conspire against her, and so on. It is perfectly wise
that she should be accompanied by a mahram when travelling, because the
purpose behind the mahram’s presence is to protect her and look after her,
especially if something bad happens. Travel exposes her to such things
regardless of how long it takes.  

Al-Nawawi (may Allaah
have mercy on him) said: The point is that whatever is known as travelling,
women are forbidden to travel without a husband or a mahram. 

The Standing Committee was asked whether it is permissible
for a woman to travel to Hajj without a mahram. They replied as follows: It
is not permissible for a woman to travel for Hajj or for any other purpose
without a mahram. 

Fataawa al-Lajnah al-Daa’imah,
11/97 

Thus it should be clear that Islam is the foremost system when it comes to protecting women and taking care of them, and respecting and honoring them, and regarding them as precious jewels that must be guarded against evil.