This is a great question to consider. Of course, the good thing about a question like this is that you can actually answer it by suggesting any character you like, as long as you can back it up from the text. Of course, this novel does contain characters who are more honest than others, and there are definitely a number who learn more about themselves as the novel progresses. In my opinion, however, the character who I feel is most honest is Soda. Consider how he gives this frank assessment of himself at the end of the novel:
Ponyboy, I'm telling you the truth. I dropped out because I'm dumb. I really did try in school, but you saw my grades. Look, I'm happy working in a gas station with cars.
Soda is the one brother who is openly able to acknowledge his feelings for his brothers and his own situation, and is happy to declare it. It is his honesty that helps Darry and Ponyboy to overcome their problems and to work on their relationship. This is why I think there is a good argument for Soda being the most honest character.