Well, it's not so much a story idea, as an idea for a type of character I'd like to play, and be paired up with. I'd like something very high fantasy, and I'd like to play an elf. A haughty and reserved elven lord, or something similar.
I'm flexible when it comes to the female counterpart, but I've always been curious about love between a nigh-immortal elf, and a mortal human, and the inevitable tragedy that would lead to. I'd also like for the woman, in that case, to be a mature one. I don't think they'd be compatible otherwise, and having a ( comparatively ) older male character just isn't something I'm too big on.
Of course, that's only one suggestion, and I'm open to alternate ideas.
I think that about covers it.