Eladrin give you a unique opportunity to explore some background options that are very seldom used.
My favorite is for my guy to be a non-combatant originally. I like my character to be run a winery, or be a carpenter or something. He is a couple of hundred years old and despite the fact he is a non-combatant by Eladrin standards, he has done more militia training in his life than most human warriors will in a lifetime.
The same goes for magic, it is quite reasonable for an Eladrin tinker or artist to know a few spells, after all, they might have spent 20 years at the university before deciding what to do with their life.
I like to play up the racial superiority aspect of the Eladarin, not by being a showoff or making out that my character is unreal, quite the opposite. I like to show off the Eladrin people, by constantly pointing out that I am not even a fighter and only made it to yellow belt in my martial training. Combined with "well of course I am better than those guys, they are not Eladrin, that is not saying much". I like to be condescending through dismissing praise, rather than seeking it.
That speaks towards a person character though, not a background story. I think you need to give some guidance yourself about your background, it really should come from you, with only a bit of help from others to spice it up.