Character exploration is usually the point of story-telling, isn't? xD
Besides, I like to clearly establish the characters' "why", their.... instrinsic motivator, I guess? It helps maintain a good momentum, even if the characters or we as writer's falter.

"What are my ultimate limits?" and "Who am I?" could both easily be explored in a sci-fi setting with other transhumanism concepts thrown in. At least, that's the first thing my mind went to.
Yet.... I'm usually steeped in sci-fi stuff, so I'm more inclined to try a setting with low-level technology.
We could just as easily do something sports-oriented and/or deal with the pressures of fame and how the public's expectations affect a celebrity psychologically (and vice-versa).

This is usually a good question to start with:
What setting sounds like the most fun to you, right now? 

(If you happen to be craving sci-fi/cyberpunk stuff, I will totally jump on the band wagon. I've just been doing a lot of that recently.)