Right before that famous scene where Jack is trying to teach Rose how to spit, they were talking about someday going to the Santa Monica Pier. According to this daydream they were sharing, Jack would teach her how to ride a horse like a “man,” which is to say with one leg on each side as opposed to sitting on the horse with both legs on the same side.

At the end of the movie, when Rose appears to be sleeping, as a grandmother, we can see the picture on her nightstand, which means that she decided to go to the pier after the accident and do what she was going to do with Jack.