Whether they're world travelers with adventurous spirits or people with highly specific missions that stop them from ever settling down, anime characters who are drifters are a great addition to any show. They open up the rest of the world to their audience, making sure that the setting never gets stale.
One example of a wandering character is Kino from Kino's Journey, who has resolved to spend her entire life traveling, only staying in a given town for three days at a time. If you prefer a show with less existentialism and more excitement, there's also Ash Ketchum and the other Pokemon trainers from Pokemon, who traverse the world trying to find every Pokemon out there and defeat gym leaders in each new city.
Which characters inspire you to hit the open road?
While Edward and Alphonse Elric do eventually settle down because Edward starts working for the Amestrian military, the two of them spend a long time with no place to call home. In fact, they're so dedicated to making sure that they don't go back to their original home that they burn it to the ground. Their wanderings are especially pronounced in the 2003 version of the series - most of the beginning is spent on them wandering the countryside looking for information about the philospoher's stone, and the series ends with the two of them parting ways to go on seperate journeys.
Naofumi Iwatani was initially summoned to Melromarc to act as one of its personal saviors, but he quickly realizes that it isn't going to work for him. Not only does Melromarc unfairly deride him as a degenerate criminal and make it impossible for him to get any work done by denying him services that are available to all of the other heroes. Besides that, he realizes that Melromarc isn't the only place in his new world that needs his help - actually, there are people all over the world who need protection from everything from government corruption to the dangerous waves he was summoned to fight in the first place.
It's not uncommon for ninja in the world of Naruto to spend months or even years travelling - after all, some of their missions can take them pretty far afield. But most ninja have a home base and a family that they try to return to whenever possible. That's not the case for Jiraiya. He spends a ton of time away from Konoha, either investigating Orochimaru, working on his books, looking after orphaned children, perfecting sage mode, or something else. Because he's constantly on the road, he was never considered for the position of Hokage, even though he's one of the most powerful ninja in Konoha.
Vash the Stampede regularly travels from town to town, rarely staying in one place for long. At first, this is because there's a huge bounty on his head due to his repeated accidental destruction of property, and he wants to avoid arrest. When the bounty is lifted because he's been legally labelled a human natural disaster, he persists in his wanderings - accompanied by two insurance agents who are there to tally up the damage he does.
He hopes that by visiting new towns, he'll be able to learn more about the two things his mother most valued: love and peace.