As regards the question, we’d like to furnish you with the following fatwa issued by the European Council for Fatwa and Research:

Regarding a woman’s travel without a mahram, this is primarily unlawful according to the hadith of the Prophet (peace and blessings be upon him): “A woman who believes in Allah and the Hereafter shall not travel for (a period of) a day and a night unless accompanied by a mahram of hers.” (Reported by al-Bukhari and Muslim)

Depending on this general text, some scholars are of the opinion that a woman should not travel by herself. Other scholars stipulate that her travel is permissible in the company of a trustworthy group of men or men and women. The prohibition conveyed by the hadith is justified by fearing that the woman may be exposed to mischief or temptation if she travels alone, bearing in mind that the dangers of travel were numerous in the past. Caliph `Umar ibn al-Khattab (may Allah be pleased with him) allowed the Prophet’s wives (Mothers of the Believers) to travel for Hajj with a group of believers and sent with them `Uthman ibn `Affan and `Abdul-Rahman ibn `Auf.
In the hadith of the Prophet (peace and blessings be upon him) to `Adiy ibn Hatim we read: “If you live long, you will see the woman travel from Hirah (a city in Iraq ) to circumambulate the Ka`bah fearing none but Allah.” (Reported by al-Bukhari)
this confirms that the cause (of the prohibition) is fear (of insecurity). If security is guaranteed and fear is no more present, a woman may travel, particularly nowadays when travel has become easy, whether by air, train or coach. In all these means of transportation, company is available and security is realized for the Muslim woman.

This is in respect of the woman’s travel from one town to another or from one country to another and her arrival on the same day of her travel, whereupon she finds company providing security. If the journey requires staying overnight in a hotel on the way, or the journey is intended to perform a certain task that requires residence for a certain period, the woman, in this case, is supposed primarily to travel with a mahram of hers, or reside for the required period with a Muslim family in that country to avoid the likelihood of temptation or mischief the woman may face.
Finally, the Council urges parents to bring up their daughters and the husbands to educate their wives according to the guidance of Allah, for a Muslim woman will certainly follow the guidance of Allah steadfastly if she has received her due amount of education and instruction and has learned the rulings and rules of Shari`ah and has comprehended her religion.”

Elaborating more on this issue, the prominent Muslim scholar, Sheikh Muhammad Iqbal Nadvi, Director and Imam of Al-Falah Islamic Center, Oakville, Ontario, Canada , states:

“As long as the woman will be in a company of trustworthy Muslim sisters and there is avoidance of any khalwah (seclusion with the opposite gender), then it is permissible. The issue is not the mahrem, rather it is the safety and security of the woman, and as long as this is secured through a trustworthy company, then it is allowed.”

With the above in mind, it becomes clear that there is nothing wrong in a woman traveling without mahram to another town or country as long as the road is safe and her safety is guaranteed and she has taken permission from her husband or parents in case she is not married and finally, her travelling is for something lawful, that is say there in nothing wrong in a woman going for vacation as long as she is going to spend the vacation along with her company in lawful acts.