Zax grew up in Gongaga, a small town that was surrounded by woods. (As seen on the 'world map'.) It contained the average small-town things.... Weapon store, place to rest, etc. It didn't have many outstanding buildings, most of the buildings were nothing more than small huts. Gongaga had one Mako reactor which later blew up, killing a few people. However, when Zax lived there, it were fine.

However, judging by Zax's attitude, I believe he would have grown bored in such a small town. That is possibly a major reason for him to go and join SOLDIER.... to go and see the world, oceans, big cities, other small towns.... and so on. He probably got along with Cloud since they both knew how it was like in a town where everybody knew everybody else.

Zax was probably liked in Gongaga, since he seemed to make friends easily, and he probably had a lot of kids and so on look up to him, like Cloud did.

So, overall, even though he probably was looked up to in his little town, I believe he's the kind of type that wants to explore the world, and not stay in a dinky little town where he would never get well known. Kind of like Riku, in Kingdom Hearts, as an example. :)