(First, it must be said that someone being a "geek" doesn't make them less of a person... It's demeaning to say otherwise, considering "geeks" are perfectly normal people as well...)
In any case, you need to do more things with her all the time, make her see that you're interested in being with her now, and that you're able to be with her now, when your competition can't be...
It's a bit of a dirty way to win someone over, admittedly, but you've got to use the advantage of having her close-by to your benefit... (And, naturally, slowly slip in comments that you enjoy spending time with her into the conversation, and such, if you want her to think of you that way...)
She may never get over her friendly/otherwise relationship with her friend hours away, and you may have to accept that, should you get further with her, but at least you'll be somewhere, by the time she should have to move away, if you press your advantage;
(At least in your case, the "rival" lives further away... My situation, the girl kept mentioning how the only previous guy to get close to her died of some heart attack or something, and kept practically comparing me to him... It got to where I felt like I had competition beyond the grave... At least you don't have that to contend with)