When Ed and Al burned down their childhood home, they'd decided that they would never stop moving forward. In some ways, that meant that they had never intended to settle down anywhere. At that time, Al hadn't had any problems with that.
Now that he was older, Al did feel the need to have a place he could call home. Someplace other than his suitcase to put old memorabilia. Someplace he could rest at when the stress of travel and work got to be too much. Someplace he could build a family.
At first, his vision of family consisted of the memories of a deceased mother, the disappearing back of an absent father, and Ed. As far as he was concerned, family meant blood relatives. It wasn't until after he'd started watching Mustang's team interact like a family that he realized that a family could consist of more than just immediate relatives. And so, over time, he began to count all the people who'd helped him and his brother as family: Mustang and his team, Teacher and Mr. Curtis, the Fort Briggs soldiers, and Winry of course.
But as Al got even older, he noticed how Ed looked at Winry differently and realized that his brother was starting to find a family all his own. Sure, Al would always be his brother, but Ed was going to someday marry Winry and maybe have some kids, and Al wasn't sure how he'd fit into that dynamic.
So, Alphonse packed his belongings in a single suitcase and crossed the desert, following an old promise to a Xingese princess and a desire to learn a new form of Alchemy.
This was the first time Al had been anywhere new without his brother or Winry, and it was a different country with a different language and a different culture. For Al, it was a new start. He had spent so long traveling as "Fullmetal's little brother," and now he got to figure out what else he could be.
After a little trial and error, he started to form a new identity in this new country. First he was "The foreigner," though soon people specified as "The Amestrian." He later became "a beginner Alkahestrists." When he got in trouble he became "a good fighter" or "an accomplished alchemist." His personal favorite though, was "the Chang princess's companion."
Being with May was kind of liberating. He found that he could be himself around her and she accepted everything about him. Sure there were disagreements and other problems sometimes, but they found their way to get through them. Before long, Al found himself figuring out who was part of his family again, and May got a special place at the top of his list.
Months turned into years, and suddenly Al found himself sitting in a house he and May could call their own. It had been a wedding present from May's grandfather, a kind of underhanded way to try and get them to stay in one place not that far from his place.
It was built in the Xingese style, something Al would have found odd when he first got to this country. It wasn't overly extravagant, but it was comfortable, with four bedroom, a decent kitchen and dining room and a nice garden. Xiao-mei and Al's cat (named, ironically enough, Panda) got accustomed to it easily.
May thought it was cozy and sweet. Al still couldn't believe he now had a house to his name.
A few years later, they were grateful for the extra bedrooms since they were filling up with kids.