I'm actually going to go against what everyone's saying and throw out ENFJ, from personal experience IRL. I know a girl who's ENFJ; she's president of student council, varsity cheerleader and CC, and is basically involved in everything. Skip to a different girl, who I know more academically; she's very smart, but she doesn't really see herself as being so, and she's not so much into studying, but does so and gets everything done on time and well.
I wouldn't be so quick to say NT because of sheer intelligence; F and T can both be "smart" but they just project their intelligence in different manners.
I don't think she'd be ENTJ; I know quite a few, including my twin, and while they do have a tendency to conquer the world, I don't really see the same attitude in the girl you're talking about.
I don't think I'd say ESTJ/ESFJ, unless she's kind of doing it more for the appearances and popularity, etc. If she's a sincerely open, cheerful person that doesn't judge, but enjoys the interaction of people, then I'd lean slightly more to ENxJ. And she does fit a lot of my ENFJ friends; diversely intelligent, sociable, enjoys leadership activities where she can work with people, and if she's sincere on top of that....yeah, I'd say ENFJ.