Ordinary surroundings can trick you into thinking your character is ordinary, because our surrounding shape much of who we are. We don't know what we're really made of until we're faced with something bigger. But what if you don't have life or death situations, or a sense of imminent danger? That doesn't mean the stakes aren't high. Perhaps your genre is young adult romance, and throwing in "danger" would feel unnatural, bordering on genre-hopping. That doesn't mean your characters should be generic.
Try this writing exercise (or just thought-exercise). Place your main character into the dangerous scenes of your favorite books. What's your main character's Hogwarts house? How would she do in the Hunger Games? What would her gift be in Crossworlds? When faced with danger, does she rely on physical strength, her brain, or her social skills? Does she run toward danger or away from it? Is she impulsive, or a planner?
This is a fun way to determine your characters strengths and weaknesses. Then, you can apply this to a real-world story, and often times, you'll get more than traits for your character. Perhaps your character is better with physical strength, and a bit impulsive. She's more likely to get into fights in school than the character who thinks through decisions and relies on intellect.
You're character doesn't have to be one thing or another, as it's not completely unrealistic for one person to be both physically strong and intelligent, but avoid too many good qualities--you don't want a Mary Sue. However, this exercise can determine which qualities are the strongest in your character. Ask yourself, in this dangerous situation, what is her first impulse?