What is it about Ponyboy that Cherry likes?
Your best bet for info on this question is chapter 2. That's when Ponyboy and Cherry first meet. Her initial impression of Ponyboy is not good, because Ponyboy is with Dally. Dally starts talking to Cherry and her friend in a rude and vulgar manner, and Cherry assumes that Ponyboy is there to do the same thing.
The girl looked at me. I was half-scared of her. I'm half-scared of all nice girls, especially Socs. "Are you going to start in on us?"
Her opinion of Ponyboy quickly softens as she realizes that Ponyboy is not a threat to her. She finds him remotely attractive too despite his young age.
"Man, your brother is one doll. I might have guessed you were brothers--- you look alike."
But I think the main reason that Cherry likes Ponyboy is because she recognizes the fact that Ponyboy is intelligent and has the potential to be a deep thinker. She sees that he is not like all of the other Greasers that she presently knows.
Cherry was looking at me. "What's a nice, smart kid like you running around with trash like that for?"
I believe it is for that reason that Cherry opens up to Ponyboy and has some fairly deep conversations with him. Cherry realizes that Ponyboy has the capacity to be more than the stereotypical Greaser, and I think that is why she develops a bond with him.