Wa `alaykum as-Salamu wa Rahmatullahi wa Barakatuh.
In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
Dear sister, thank you for your question and for your interest to adhere to the teachings and rulings of Islam.
It is allowed for a girl to travel to another country for study on two conditions; the approval of her family and being safe concerning herself, religion, and properties.
Responding to you question, Sheikh Kifah Mustapha, the Imam and Associate Director at the Mosque Foundation, one of the largest Islamic Centers in Chicago, states,
The answer has two perspectives; Shari`ah and family:
From the Shari`ah point of view, I lean toward the point of view that the reason behind requiring a mahram for woman’s travel is related to safety. The proof for that is the hadith in which the Prophet (peace and blessings be upon him) told the `Adi ibn Hatim just before he embraced Islam, “If you live long, you will certainly see that a lady traveling from al-Hira till (safely reach Makkah and) perform the Tawaf around the Ka`bah, fearing none but Allah.” (Al-Bukhari)
Also the school of Shafi`yyah allowed women to travel for Hajj with the company of other trusted women.
Bearing this in mind, if you are to live in a trusted area, in a respectful college where reputation is great for safety, separated rooms from other gender, prohibition of intoxicants on campus, presence of other Muslim trusted sisters and connecting with local Mosques Imams, I feel comfortable to say it should be allowed to study alone in a different town. But at any time any of these conditions are not valid, the sister must reconsider the decision.
The second part is that you have to get the permission of your family too as a condition. Obeying parents in such matters is an honorable thing.
Allah Almighty knows best.