A Geek Girl is not necasserily unpopular; quite often they will enjoy the same activities as 'normal' people do (ie. going out drinking, chilling, partying) but they also enjoy other things, that these 'normals' may not.
Geek girls enjoy logo t-shirts, video games, anime (some of them), fanfiction, reading, fangirling, writing and pop culture references.
They quite often have a good sense of humour and are interesting, intellectual (when they want to be) people.
Often Geek Girls can fit into a group of 'normal' girls easily. Sometimes it may come as a suprise that they are geeks. But the term for geek has broadened and often, Geeks are simply regarded as the cool people who simply live life the way they want.
There are hardcore geek girls, but these may often blur into the socially awkward nerds.
Geek Girl (on facebook): Time to go home and play Dragon Age!
Amanda Siefrieds character in Jennifers body is a prime example of a geek girl.