All it takes is some self confidence and a willingness to broaden one's interests and you will be surprised what sorts of people you meet. Yes, I think geeks should try to meet their opposite (a non-geek) and they should try to be more broad of a human being than just a "nerd" with a narrow focus.
I took up singing for example even though I work in a completely unrelated field for my day job. I also dabble in video and photography in my spare time.
Success in life is all about taking chances. You cannot spell success without "suc"-k so you are not going to succeed at everything the first time.
That geeky girl probably already has a man in her life who isn't a geek so male geeks should not expect to be able to have a geeky girlfriend nor should they all want to have one.