Here’s the thing. I think in the books Arya travels, but i also think she settles down eventually. She names her wolf after Nymeria who lead her people to Dorne and married the prince there so her people will be safe.
“We are in part, Your Grace. Nymeria's blood is in me, along with that of Mors Martell, the Dornish lord she married. On the day they wed, Nymeria fired her ships, so her people would understand that there could be no going back. Most were glad to see those flames, for their voyagings had been long and terrible before they came to Dorne, and many and more had been lost to storm, disease, and slavery. There were a few who mourned, however. They did not love this dry red land or its seven-faced god, so they clung to their old ways, hammered boats together from the hulks of the burned ships, and became the orphans of the Greenblood. The Mother in their songs is not our Mother, but Mother Rhoyne, whose waters nourished them from the dawn of days." - the Queenmaker
Arya, herself, is named after Arya Flint of the Mountain Clans. Arya Flint wed Rodrik Stark who was known as the Wandering Wolf.
