According to Amy Kelly in her Eleanor and the Four Kings, what remained of the Western Empire at the time wasn't much of a place for a young woman, either:

"If the sojourn among the shrines of Byzantium was a nine days' wonder to the king, it was an awakening experience for the queen, whose education had progressed just far enough to make her travels profitable. It opened her eyes to vast, lofty, undreamed-of possibilities for majesty, and all the accidia 1 from which she had suffered at home was purged from her soul. The magnificent entertainment of the crusaders in Manuel's capital was of a nature to fire the imagination of the young Queen of France. The reality was far above the rumor, and every way extravagant. She learned that Paris was not, as she had been taught by her clerks, the highest of all places in Christendom. Byzantium, set in its pomp of water and of light, was not only incredibly vaster; it was infinitely more refined. The famous city had inherited much of the outward grandeur of ancient Rome, but was as well a treasury of artistic marvels that had drifted down to the Bosporus from Persia and Cathay, from Baghdad and Mosul..." 2

Had a part of her been left behind in this Holy Land after the fateful crusade of her Pious First Husband? Was there a fusion between her inherited ambitious nature and the subtler, more refined manners of the Imperial Court (which moved "with the supernal majesty and order of the heavenly constellations" 3) that would later provide the inspiration for her seditious "Tribunals of Love?"

Am wondering, too, if the country of origin is "no country for old men," perhaps Byzantium with all its beyond the wildest dreams of even a princess glories could be "no place for a young woman" for all the disappointment it would later set up for.

Sailing To Byzantium

I

That is no country for old men. The young
In one another’s arms, birds in the trees
—Those dying generations—at their song,
The salmon-falls, the mackerel-crowded seas,
Fish, flesh, or fowl, commend all summer long
Whatever is begotten, born, and dies.
Caught in that sensual music all neglect
Monuments of unageing intellect.

II

An aged man is but a paltry thing,
A tattered coat upon a stick, unless
Soul clap its hands and sing, and louder sing
For every tatter in its mortal dress,
Nor is there singing school but studying
Monuments of its own magnificence;
And therefore I have sailed the seas and come
To the holy city of Byzantium.

III

O sages standing in God’s holy fire
As in the gold mosaic of a wall,
Come from the holy fire, perne in a gyre,
And be the singing-masters of my soul.
Consume my heart away; sick with desire
And fastened to a dying animal
It knows not what it is; and gather me
Into the artifice of eternity.

IV

Once out of nature I shall never take
My bodily form from any natural thing,
But such a form as Grecian goldsmiths make
Of hammered gold and gold enamelling
To keep a drowsy Emperor awake;
Or set upon a golden bough to sing
To lords and ladies of Byzantium
Of what is past, or passing, or to come.

-William Butler Yeats

***
1. Melancholy, sadness, immobility.
2. Kelly, pp.42-43
3. Kelly, pg. 43.