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Actually they have a pretty healthy relationship.
Ofc Takagi teases him a lot, but it is never really mean nor does she try to embarrass Nishikata in public. It's like the teasing between good friends and more of a contest or friendly rivalry. Also, if he would really dislike it he could have already told here to fuck off or simply tried to avoid her. But they still go to school and spend their holidays together.
It's pretty obvious that they like each other. When I read the first chapters I thought Takagi was just another tsundere, but I was wrong. In fact she knows her feelings towards Nishikata pretty good, but she wants him to make the first step (or at least let it look like he made the first step. Take the summer festival, for example). Nishikata on the other hand isn't so sure about his feelings and therefore his constant tries to get back on Takagi might be in fact a result of his confusion.
Both like each other pretty much, but none of them is able to directly admit it, probably because they are afraid of rejection. So Takagi wants Nishikata to make the first and Nishikata...well, he doesn't really know what he wants.
But thats just my opinion. Post pictures.
