Have you considered the fourth option?
To develop a closer friendship with this girl (no ulterior motives) and see where a friendship leads the two of you in the future?
By not having anything to do with this girl because she won't go out with you could be costing you a friendship you wouldn't have wanted to live without.
Also, by being friends with her (on a more personal level than just the social scene) you may also discover she'd be your worst nightmare as someone to have a relationship with.
