Without going and posting major pieces of the book and getting in trouble for it, you need to read the Pathfinder Companion book: Elves of Golarion.
Faction? Is this for Pathfinder Society? If not: What exactly do you mean with faction?
Other than that, there are some elves more or less everywhere on Golarion. There aren't that many elven strongholds any more. Kyonin is an elven nation (well, the elven nation actually), and you can find elves in Varisia (a lot of wilderness there, nice if you don't like crowds of humans around), especially the Miarani forest. Those are good places for wood elves.
I guess elves become adventurers for the same reasons as everybody else: They're thrill seekers, they hunger for glory and riches, they don't fit in at home, or adventure chooses them....
With elves, there is another possibility: the Forlorn. Forlorn are elves that grew up among humans, outside of sheltered elven society. Having human playmates and watching them grow up, grow old, and die, all in less time than it takes you to reach adulthood... apparently that drives you nuts. Forlorn are often warped. A large percentage of Forlorn become adventurers, because that way, you're always around and don't form lasting friendships with people, and death is your constant companion, you kinda get used to it.