Oates describes Connie as only half-aware, saying she's "dreaming" and her mother must "drag her back into the daylight." What is so appealing to...

Connie is 15 years old and is concerned with only boys, music, and her appearance.  She is manipulative and deceitful, as well, and loves attention to be showered upon her by boys.  Unfortunately, Connie is not rooted in reality. She lets her vain nature overtake her judgment in some instances.  She seems to flit through life with superficiality.  Beyond her own interests, Connie does not seem to be concerned about anyone else.  

Connie's inability to be rooted in reality is part of what leads to her demise (or supposed demise, I should say) at the hands of Arnold Friend.  When Arnold appears at her home, she does not react quickly enough to be able to get help and does not realize that he is dangerous until it is too late.  She has let her own jaded view of things prevent her from seeing the reality of the dangerous nature of this man until it is too late to save herself, although she does leave with Arnold Friend in order to save her family's lives.  

Her half-conscious world is appealing because in this type of world, one can ignore problems of others and the world around them.  He or she is not conscious of the stark reality surrounding him or her.  Connie glides through her days obsessing about boys and her outer appearance, choosing not to deal with the real world.