All perfect praise be to Allah
Sister, it's actually excellent that you are concerned about this issue and seeking solution in light of shariah.
Coming to the question, it seems you already know and it does not need any more clarification that traveling without a mahram is not allowed for women, even they cannot go to hajj without a mahram, if mahram is not available for a woman and she has all the resources and will to do hajj, she still cannot perform hajj without mahram (some fuqaha make exception specially for the hajj traveling with some trusty people with consent of mahram though this exception is not said to be for any other kind of traveling until or unless necessary enough to make an exception).
So, its like you want to follow shariah, but you are not liking some of its rule, this is where the real test is. Keeping aside the argument of teach where you live etc, still! we have to follow shariah in all aspects of our lives. Something which you know shariah is clear about, and you don't like it, this is no excuse or exception for that law of shariah.
If you leave something you like for the will of Allah, he will surely give you something better, in this world and in hereafter.
Let's have some quotes :) :
Allah says in Quran:
Indeed, Allah has purchased from the believers their lives and their
properties [in exchange] for that they will have Paradise. They fight
in the cause of Allah , so they kill and are killed. [It is] a true
promise [binding] upon Him in the Torah and the Gospel and the Qur'an.
And who is truer to his covenant than Allah ? So rejoice in your
transaction which you have contracted. And it is that which is the
great attainment. Quran 9/111
And in a hadeees it says:
Abu Huraira reported: The Messenger of Allah, peace and blessings be
upon him, said, “The world is a prison for the believer and a paradise
for the unbeliever.”
Source: Ṣaḥīḥ Muslim 2956
These quotes are clear that a believer is not supposed to follow his own wills in this world, if he want to succeed in hereafter. It's a trade, a very profitable trade. Giving up something in this temporary world for hereafter which is never ending life, and where you can do whatever you want!
And whosoever puts his trust in Allâh, then He will suffice him. Surat
And in hadees quoted in musnad imam ahmed bin humbal
The messenger of Allah صلی اللہ علیہ وسلم said “You will never leave
something for the sake of Allah, but Allah will give you something
better in return.”
Another ayah, Allah describes reward for the people who believe and follow his commandments.
He prepared for you in which there is that which no eye has seen no
ear has heard and it has never crossed the mind of man. [bukhari] you
will have there whatever your heart desire. Surah al-Nahl 16:31
By these, i want you to put your trust in Allah, that if you leave something for the sake of Allah, he will surely replace that with something better.
As conclusion, there is no exceptional case for which the law of shariah can be avoided. So, you HAVE to follow shariah and either not travel(and live there) without a mahram, or look up for a mahram who has matching passion or lives there or anything.
May Allah give you best reward for your efforts.
Allah knows best