Na verdade, está bem estabelecido nos livros como e por que Arya terminou em A Casa de Preto e Branco, Bravos.
TL; DR
Logo após o cão ter uma ferida mortal e Arya parte com ele, ela chega em uma pequena cidade Saltpans . Ela quer ir até a Muralha, porque Jon Snow está lá. Ela compra sua passagem em uma galleas de Braavosi com a moeda de ferro dada a ela por Jaqen. Mas o capitão se recusa a navegar para o norte, então ela acaba em Braavos. Em Braavos, ela visita a casa do preto e branco e procura Jaqen para aprender a arte de ser um assassino. E ela quer sangue e vingança.
Agora, a resposta longa, com as citações do livro.
ASOS, capítulo 74, Arya.
“I want to see the captain,” Arya told him. He only shouted louder. But the commotion drew the attention of a stout grey-haired man in a coat of purple wool, and he spoke the Common Tongue. “I am captain here,” he said. “What is your wish? Be quick, child, we have a tide to catch.”
“I want to go north, to the Wall. Here, I can pay.” She gave him the purse. “The Night’s Watch has a castle on the sea.”
“Eastwatch.” The captain spilled out the silver onto his palm and frowned. “Is this all you have?”
It is not enough, Arya knew without being told. She could see it on his face.
... ... ...
“Wait,” Arya said suddenly. “I have something else.” She had stuffed it down inside her smallclothes to keep it safe, so she had to dig deep to find it, while the oarsmen laughed and the captain lingered with obvious impatience. “One more silver will make no difference, child,” he finally said.
“It’s not silver.” Her fingers closed on it. “It’s iron. Here.” She pressed it into his hand, the small black iron coin that Jaqen H’ghar had given her, so worn the man whose head it bore had no features. It’s probably worthless, but . . . The captain turned it over and blinked at it, then looked at her again. “This . . . how . . . ?”
Jaqen said to say the words too. Arya crossed her arms against her chest. “Valar morghulis,” she said, as loud as if she’d known what it meant.
“Valar dohaeris,” he replied, touching his brow with two fingers. “Of course you shall have a cabin.”
Foi assim que Arya comprou sua passagem. Mas a que lugar, isso é revelado no próximo capítulo.
AFFC, capítulo 6, Arya
Arya stood at the prow, one hand resting on the gilded figurehead, a maiden with a bowl of fruit. For half a heartbeat she let herself pretend that it was her home ahead.
But that was stupid. Her home was gone, her parents dead, and all her brothers slain but Jon Snow on the Wall. That was where she had wanted to go. She told the captain as much, but even the iron coin did not sway him. Arya never seemed to find the places she set out to reach. Yoren had sworn to deliver her to Winterfell, only she had ended up in Harrenhal and Yoren in his grave. When she escaped Harrenhal for Riverrun, Lem and Anguy and Tom o’ Sevens took her captive and dragged her to the hollow hill instead. Then the Hound had stolen her and dragged her to the Twins. Arya had left him dying by the river and gone ahead to Saltpans, hoping to take passage for Eastwatch-by-the-Sea, only . . .
Braavos might not be so bad. Syrio was from Braavos, and Jaqen might be there as well. It was Jaqen who had given her the iron coin. He hadn’t truly been her friend, the way that Syrio had, but what good had friends ever done her?
É assim que ela acaba em Braavos.
E novamente no mesmo capítulo, quando ela entra na Casa de Preto e Branco, ela tem a seguinte conversa com um homem idoso, mais tarde chamado de "o homem gentil".
“What place is this?” she asked him.
“A place of peace.” His voice was gentle. “You are safe here. This is the House of Black and White, my child. Though you are young to seek the favor of the Many-Faced God.”
“Is he like the southron god, the one with seven faces?”
“Seven? No. He has faces beyond count, little one, as many faces as there are stars in the sky. In Braavos, men worship as they will . . . but at the end of every road stands Him of Many Faces, waiting. He will be there for you one day, do not fear. You need not rush to his embrace.”
“I only came to find Jaqen H’ghar.”
“I do not know this name.”
Her heart sank. “He was from Lorath. His hair was white on one side and red on the other. He said he’d teach me secrets, and gave me this.” The iron coin was clutched in her fist. When she opened her fingers, it clung to her sweaty palm.
Ela está lá para Jaqen e ela quer aprender. E quanto a sua motivação, novamente neste mesmo capítulo.
“Do you fear death?”
She bit her lip. “No.”
“Let us see.” The priest lowered his cowl. Beneath he had no face; only a yellowed skull with a few scraps of skin still clinging to the cheeks, and a white worm wriggling from one empty eye socket. “Kiss me, child,” he croaked, in a voice as dry and husky as a death rattle.
Does he think to scare me? Arya kissed him where his nose should be and plucked the grave worm from his eye to eat it, but it melted like a shadow in her hand.
The yellow skull was melting too, and the kindliest old man that she had ever seen was smiling down at her. “No one has ever tried to eat my worm before,” he said. “Are you hungry, child?”
Yes, she thought, but not for food.
Ela quer vingança. Ela está com fome de sangue.